PAUL draws up a roll of honour and of dishonour of his friends.  Some are only names to us; of some, as we read the Acts of the Apostles as well as the Epistles, we get the occasional revealing glimpse. If we are allowed to use our imagination, we can reconstruct some of the stories. ~Barclay commentary

Now to the other commentaries. We will begin with the general and go to the specific.

We will begin with Matthew Henry and its discussion of verses 14 and 15.

He mentions Alexander, and the mischief that he had done him, 2 Timothy 4:14-15. This is he who is spoken of Acts 19:33. It should seem, he had been a professor of the Christian religion, a forward professor, for he was there particularly maligned by the worshippers of Diana, and yet he did Paul much evil. Paul was in as much danger from false brethren (2 Corinthians 11:26) as from open enemies. Paul foretells that God would reckon with him. It is a prophetical denunciation of the just judgment of God that would befall him: The Lord will reward him according to his works. He cautions Timothy to take heed of him: “Of whom be thou aware also, that he do not, under pretence of friendship, betray thee to mischief.” It is dangerous having any thing to do with those who would be enemies to such a man as Paul. Observe,

(1.) Some who were once Paul's hearers and admirers did not give him reason to remember them with much pleasure; for one forsook him, and another did him much evil, and greatly withstood his words. Yet,

(2.) At the same time he mentions some with pleasure; the badness of some did not make him forget the goodness of others; such as Timothy, Titus, Mark, and Luke.

(3.) The apostle has left a brand on the names and memory of two persons; the one is Demas, who forsook him, having loved the present world, and the other is Alexander, who greatly withstood his words.

(4.) God will reward evil-doers, particularly apostates, according to their works.

(5.) Of such as are of Alexander's spirit and temper we should beware; for they will do us no good, but all the mischief that is in their power. ~Matthew Henry Main

Quoted verses:
Acts 19:33
And they drew Alexander out of the multitude, the Jews putting him forward. And Alexander beckoned with the hand, and would have made his defence unto the people.

2 Corinthians 11:26
In journeyings often, in perils of waters, in perils of robbers, in perils by mine own countrymen, in perils by the heathen, in perils in the city, in perils in the wilderness, in perils in the sea, in perils among false brethren;

Now to the Matthew Henry Concise which covers verses 14-18.

There is as much danger from false brethren, as from open enemies. It is dangerous having to do with those who would be enemies to such a man as Paul. The Christians at Rome were forward to meet him, Acts 28, but when there seemed to be a danger of suffering with him, then all forsook him. God might justly be angry with them, but he prays God to forgive them. The apostle was delivered out of the mouth of the lion, that is, of Nero, or some of his judges. If the Lord stands by us, he will strengthen us in difficulties and dangers, and his presence will more than supply every one's absence. ~Matthew Henry Concise

The rest of the commentaries I have are the specific type. It is easy to see that this verse is broken out in two parts.

1] Alexander the coppersmith did me much evil.
2] The Lord reward him according to his works.

1] Alexander the coppersmith did me much evil.

Notice this from the Cambridge Bible [commentary].

Alexander the coppersmith did me much evil - The Greek word has a technical meaning, ‘impeached,’ ‘indicted,’ and so it is sometimes rendered here ‘laid many grievous things to my charge’; but it is in the simpler sense, ‘shewed me much mischief,’ that the verb is used nine times by Paul. Cf. 1 Timothy 1:16, Titus 2:10; Titus 3:2.  ~Cambridge Bible [commentary]

Quoted verses:
1 Timothy 1:16 [see Lesson]
Howbeit for this cause I obtained mercy, that in me first Jesus Christ might shew forth all longsuffering, for a pattern to them which should hereafter believe on him to life everlasting.

Titus 2:10
Not purloining [stealing or keeping back; embezzle], but shewing all good fidelity; that they may adorn the doctrine of God our Saviour in all things.

Titus 3:2
To speak evil of no man, to be no brawlers, but gentle, shewing all meekness unto all men.

People's New Testament:

Alexander the coppersmith. - An Alexander is named in Acts 19:33 and in 1 Timothy 1:20 as belonging to Ephesus. This may have been the same man. We cannot be sure whether the evil was done in Ephesus, or Rome. ~People's New Testament

Did me much evil. - By his opposition. ~People's New Testament

Did me much evil - Literally shewed me much ill-treatment. ~Vincent's Word Studies

Alexander the coppersmith. - Old word, only here in N.T., for metal-worker (copper, iron, gold, etc.). Possibly the one in 1 Timothy 1:20, but not the one in Acts 19:33. unless he afterwards became a Christian. ~Robinson's Word Pictures

Quoted verses:
1 Timothy 1:20 [see Lesson]
Of whom is Hymenaeus and Alexander; whom I have delivered unto Satan, that they may learn not to blaspheme.

Acts 19:33 ...quoted above

Did me much evil. - Evidently he had some personal dislike towards Paul and possibly also he was a Gnostic. ~Robinson's Word Pictures

Alexander the coppersmith — or “smith” in general. Perhaps the same as the Alexander at Ephesus. Excommunicated then he subsequently was restored, and now vented his personal malice because of his excommunication in accusing Paul before the Roman judges, whether of incendiarism [arson] or of introducing a new religion. He may have been the Alexander put forward by the Jews in the tumult at Ephesus (Acts 19:33-34). ~Jamieson, Fausset, Brown

Alexander the coppersmith - Or, rather, “the brazier” - ὁ χαλκεύς ho chalkeus. The word is used, however, to denote a worker in any kind of metals. This is probably the same person who is mentioned in 1 Timothy 1:20, and perhaps the same as the one mentioned in Acts 19:33. ~Barnes Notes

Quoted scriptures:
1 Timothy 1:20 ...quoted above

Acts 19:33 ...quoted above

Alexander the coppersmith - We are not to understand this of any tradesman, but of some rabbin; for it was not unusual for the Jews to apply the name of some trade as an epithet to their rabbins and literary men. He is, in all probability, the very same mentioned Acts 19:33; and it is not unlikely that he may have been the same whom the apostle was obliged to excommunicate, 1 Timothy 1:20. ~Adam Clarke

Alexander the coppersmith did me much evil - This seems to be the same person that was at Ephesus in the tumult, when the apostle was there, Acts 20:33 and whom he afterwards delivered to Satan, along with Hymenaeus, for blasphemy, 1 Timothy 1:20. It was very likely he had lately been at Rome, though now returned to Ephesus, and had done great injury to the apostle's character, and had reproached and reviled him as a man of bad principles and practices; his business is mentioned, to distinguish him from any other of that name, and to show the insolence of the man, that though he was an illiterate person, and in such a mean station of life, yet took upon him to resist the apostle and his doctrine. ~John Gill

Quoted verses:
Acts 20:33
I have coveted no man's silver, or gold, or apparel.

1 Timothy 1:20 ...quoted above

2] The Lord reward him according to his works.

The Lord reward him according to his works. - The aorist optative has less weight of ms. authority than the future indic, will render, which tense of the same verb has occurred 2 Timothy 4:8. ~The Cambridge Bible [commentary]

Quoted verse:
2 Timothy 4:8 [see Lesson]
Henceforth there is laid up for me a crown of righteousness, which the Lord, the righteous judge, shall give me at that day: and not to me only, but unto all them also that love his appearing.

The Lord reward him. - The Christian, when wronged, is to turn over to the Lord the recompense for the wrong. ~People's New Testament

The Lord will reward him - This he spoke prophetically. ~John Wesley Explanatory Notes

The Lord will reward him - More correctly shall reward. ~Vincent's Word Studies

The Lord will reward him - Future active of the same verb used in 2 Timothy 4:8, but with a very different atmosphere. ~Robinson's Word Pictures

Quoted verse:
2 Timothy 4:8  ...quoted above

The Lord will reward him - The oldest manuscripts read, “shall reward,” or “requite him.” Personal revenge certainly did not influence the apostle (2 Timothy 4:16-22). ~Jamieson, Fausset, Brown

Quoted verse:
2 Timothy 4:16-21 [see Lesson]
16 At my first answer no man stood with me, but all men forsook me: I pray God that it may not be laid to their charge.
17 Notwithstanding the Lord stood with me, and strengthened me; that by me the preaching might be fully known, and that all the Gentiles might hear: and I was delivered out of the mouth of the lion.
18 And the Lord shall deliver me from every evil work, and will preserve me unto his heavenly kingdom: to whom be glory for ever and ever. Amen.
19 Salute Prisca and Aquila, and the household of Onesiphorus.
20 Erastus abode at Corinth: but Trophimus have I left at Miletum sick.
21 Do thy diligence to come before winter. Eubulus greeteth thee, and Pudens, and Linus, and Claudia, and all the brethren.
22 The Lord Jesus Christ be with thy spirit. Grace be with you. Amen.

The Lord reward him according to his works. - compare the notes at 1 Timothy 1:20. This need not be regarded as an expression of private feeling; still less should it be understood as expressing a desire of revenge. It is the language of one who wished that God would treat him exactly as he ought to be treated, and might be in accordance with the highest benevolence of any heart. It is the aim of every just government that every one should be treated exactly as he deserves; and every good citizen should desire and pray that exact justice may be done to all. It is the business of a police officer to ferret out the guilty, to bring them to trial, to secure a just sentence; and any police officer might “pray,” with the utmost propriety, that God would assist him in his endeavors, and enable him to perform his duty. This might be done with no malevolent feeling toward any human being, but with the purest love of country, and the most earnest desire for the welfare of all. ~Barnes Notes

The Lord reward him - Αποδῳη αυτῳ ὁ Κυριος· But instead of αποδῳη, which has here the power of a solemn imprecation, αποδωσει, he will reward, is the reading of the very best MSS., several of the versions, and some of the chief Greek fathers. This makes the sentence declaratory: The Lord Will reward him according to his works. This reading is most like the spirit and temper of this heavenly man [like Christ]. See 2 Timothy 4:16. ~Adam Clarke

Quoted verse:
2 Timothy 4:16 [see Lesson]
At my first answer no man stood with me, but all men forsook me: I pray God that it may not be laid to their charge.

The Lord reward him according to his works - which may be considered either as an imprecation [im-pri-key-shuh n--cursing] upon him, as knowing him to be a wicked blasphemer, and a reprobate person; and which arose, not from private resentment, and on account of the private injury he had done to him; but from a pure zeal for the glory of God, and the honour of his name, without mingling his own spirit and passions with it: or as a prophecy, or declaration of what would be; and so the Alexandrian copy, and the Vulgate Latin and Syriac versions, read, "the Lord will render to him." ~John Gill

If you do a study on the second half of this verse, "the Lord reward him according to his works" you will see a controversy as to whether Paul was upset with Alexander and was seeking revenge on him via God. As we saw in the commentaries on this second part of the verse, such was not the case. Notice some linked scriptures.

1 Samuel 24:12
The LORD judge between me and thee, and the LORD avenge me of thee: but mine hand shall not be upon thee.

2 Samuel 3:39
And I am this day weak, though anointed king; and these men the sons of Zeruiah be too hard for me: the LORD shall reward the doer of evil according to his wickedness.

Psalm 28:3-4
3 Draw me not away with the wicked, and with the workers of iniquity, which speak peace to their neighbours, but mischief is in their hearts.
4 Give them according to their deeds, and according to the wickedness of their endeavours: give them after the work of their hands; render to them their desert.

Jeremiah15:15
O LORD, thou knowest: remember me, and visit me, and revenge me of my persecutors; take me not away in thy longsuffering: know that for thy sake I have suffered rebuke.

Jeremiah 18:19-23
18 Then said they, Come, and let us devise devices against Jeremiah; for the law shall not perish from the priest, nor counsel from the wise, nor the word from the prophet. Come, and let us smite him with the tongue, and let us not give heed to any of his words.
19 Give heed to me, O LORD, and hearken to the voice of them that contend with me.
20 Shall evil be recompensed for good? for they have digged a pit for my soul. Remember that I stood before thee to speak good for them, and to turn away thy wrath from them.
21 Therefore deliver up their children to the famine, and pour out their blood by the force of the sword; and let their wives be bereaved of their children, and be widows; and let their men be put to death; let their young men be slain by the sword in battle.
22 Let a cry be heard from their houses, when thou shalt bring a troop suddenly upon them: for they have digged a pit to take me, and hid snares for my feet.
23 Yet, LORD, thou knowest all their counsel against me to slay me: forgive not their iniquity, neither blot out their sin from thy sight, but let them be overthrown before thee; deal thus with them in the time of thine anger.

Acts 7:59-60
59 And they stoned Stephen, calling upon God, and saying, Lord Jesus, receive my spirit.
60 And he kneeled down, and cried with a loud voice, Lord, lay not this sin to their charge. And when he had said this, he fell asleep.

2 Thessalonians1:6
Seeing it is a righteous thing with God to recompense tribulation to them that trouble you;

2 Timothy 4:16 [see Lesson]
At my first answer no man stood with me, but all men forsook me: I pray God that it may not be laid to their charge.

1 John 5:16
If any man see his brother sin a sin which is not unto death, he shall ask, and he shall give him life for them that sin not unto death. There is a sin unto death: I do not say that he shall pray for it.

Revelation 6:10
And they cried with a loud voice, saying, How long, O Lord, holy and true, dost thou not judge and avenge our blood on them that dwell on the earth?

There is nothing wrong in Paul creating this roll of honor and dishonor.  Even with his enemies, Paul puts everything into God's hands.  Saving the one action of false doctrine, he does not go into a vicious, detailed attack on Alexander.  In addition, Paul does not curse him or seek personal revenge.  He puts judgment of Alexander into the hands of God.

These are the lessons of verse 14.