A “cloke” (v.13) is not a coat (cf. Lu. 6:29), it was more like a mantle or a shawl. Paul left his cloke with Carpus in Troas, where Paul had to raise a man from the dead who had fallen asleep and fell out a third story window (Acts 20:1-16). But Paul probably didn’t forget the cloke in all the excitement. He had chosen to walk from Troas to Assos on a warm day and probably sent the cloke with Timothy, who went by ship, and somehow they never connected.
So Paul wasn’t asking Timothy to go 200 miles out of his way to get the cloke before coming to see him, he was just asking for him to bring it with him from Ephesus. It is important to let other members of the Body of Christ minister to us, especially when it is not inconvenient for them!
Paul also left some “books” (v.13) in Troas. Those could be the books of his Bible (cf. Dan. 9:2), but it is more likely books about the Bible, since he asked Timothy “especially” to bring “the parchments” (v.13), which were probably his Bible. Either way, Paul read books about the Bible and encouraged Timothy to do so also (I Tim. 4:13). If even Paul read more than just the Bible itself, we probably should too!
Of course, the parchments could have been blank, and Paul could have been asking for them “especially” to write more epistles. He was burdened with “the care of all the churches” II Cor. 11:28) and planned to keep ministering to his last breath, even though he was in prison on Death Row (4:6). His hand clave to the sword of the Spirit (II Sam. 23:9,10).
Since Paul warned Timothy to be ware of Alexander the coppersmith (v. 14,15), he was probably the Alexander of Ephesus where Timothy was (Acts 19:28-34), the man “of like occupation” with the silversmiths. The mob was going to kill Paul for saying there are no gods made of silver, so the Jews put Alexander forward to show that one of their own didn’t object to idolatry. He “withstood” Paul’s words by imitating them (cf. I Tim. 3:8). If he was willing to sell out Judaism for money, he was probably willing to sell out Paul’s message for money once he learned it (Tit. 1:10,11).
When Paul says Alexander “did me much evil” by withstanding his words, it showed he took it personally. But he was willing to let the Lord reward him (v.14) as He said he would (I Cor. 3:14; II Cor. 5:10). That’s an example of Paul praying God would do what He said He would, which is a good way to pray. For example, the Lord promises to always be with us, but Paul still prayed He would be (II Tim. 4:22).
Of course, if Alexander wasn’t saved, he’ll still be judged “according to his works” at the Great White Throne (Rev. 20:12). We should let God do all the judging of unsaved homosexuals, abortionists, etc. We’re here to help save them, not judge them (cf. Luke 9:53-56).
Paul’s “first answer” (v.16) was his first answer in court (cf. Acts 26:16). None of the 27 people Paul said hello to in Romans 16 stood with him in that Roman court appearance. Sometimes you have to stand alone for the truth!
The Lord always “strengthens” His people (4:17 cf. Ps. 37:39)), but under the Law He also promised to deliver them if they were righteous (Ps. 37:39,40). Paul was righteous, but wasn’t under that law (Rom. 6:15). But God delivered him at his first answer because He always delivered His prophets until they could deliver His message (cf. Jer. 15:20,21). He delivered Paul in the past (Acts 18:9,10; 23:11) and at his first answer so he could be released from his first imprisonment so the preaching of the mystery could be fully known among the Gentiles (4:17).
The “lion” could be a literal lion, since history tells us that Christians were often fed to the lions, but it could also be the devil (I Pe. 5:8). But Satan is more of an angel of light today (II Cor. 11:14), so I think the lion was the king who had him in prison, since kings are often called lions (Pr. 19:12; 20:2; Jer. 50:17; Ezek. 32:2).
Paul was executed shortly after saying the Lord would deliver him (4:18). Was he mistaken? No, God delivered Him eternally to his “heavenly kingdom” (4:18 cf. I Cor. 15:50). He couldn’t heal Trophimus (4:20) because the gift of healing had ceased by that time, and all other gifts.