1. Whereas Lucius was a Jew, Keener (p404) thinks that Col 4:11,14 favours Luke being a Gentile. However, in my last post I argued that Col 4:11, 14 confirms that Luke was a Jew.
2. Following Fitzmyer, Keener points out that the name is spelled differently in Rom 16:23 than in Phlm 24; Col 4:14 (p404 n17). However, this is not surprising. "Luke" is a hypocoristic form of the name "Lucius" and hypocoristic name-forms abound in Philemon and Colossians (Epaphras, Demas), perhaps because the greeters had visited Colossae and had a close relationship with the believers there. Romans, on the other hand, was not written to a city that the greeters had visited, so familiar, abbreviated name-forms would not be appropriate. The greeters had, on their travels, met some believers who subsequently moved to Rome, but they had not met the majority of the audience. Thus Sosipater has his full name-form in Rom 16:21, and the shortened form, Sopater, in Acts 20:4.
3. Keener (p1987n52) notes the view of e.g. Dunn that someone as important as the Lucius of Acts 13:1 would be given a fuller description than that given to the Lucius of Rom 16:21. However, Dunn overlooks the importance of name order. In the list of Greeters, Lucius is named second only to Timothy. This suggests that he had travelled extensively among the churches for many years and had thereby met many who had moved to Rome. It seems that he knew more members of the church of Rome than any of the greeters except Timothy. His position in the list shows that he was prominent and his absence from Acts would be surprising (unless he is the author).
4. Keener correctly argued that Luke may have been present for events where he does not use "we" (as well as events where he does use "we") (p2363-74). However, he back-slides from this conclusion on pages 1987, 2531, 2957, and 2954 where he writes,
Paul there[in Rom 16:21] lists greetings from his coworkers, mentioning Timothy, Lucius (possibly but not necessarily our Luke; the "we" resumes only in Acts 20:5)But the original plan was for Paul and his companions to sail to Syria directly from Achaia, so it is highly likely that the author of acts assembled, with the others, in Achaia. We should therefore expect to find his name in Rom 16:21-23 since he would know many of the members of the church of Rome. Keener avoids the problem by suggesting, without evidence, that Luke changed his mind about whether to accompany the collection. Keener (p2958) writes,
This may have been a late decision based on Paul's change of course; Macedonia's contribution was complete (cf. 20:3), and Luke could have planned to stay on in Philippi until he learned that Paul was passing through Macedonia en route to Jerusalem.This is a desperate move by Keener. Luke had long known about the collection, for Paul had passed through Macedonia on his way to Achaia. Why would Luke decide not to participate in the journey, and then change his mind later?
In conclusion, Keener's tentative decision to distinguish between Lucius and Luke is not well founded.
My own earlier post arguing that Lucius was Luke and also the author of Acts is here.