What does it mean for the Macedonian churches to give first to the Lord? Is that contrasted with giving to Paul, by the καὶ ἡμῖν? Is the giving to the Lord the Paul's collection for Jerusalem? Is it giving to the local church? Are there elements of the passage that helps us identify this meaning?
Well from the context the Apostle Paul was praising the churches of Macedonia despite their great trial of affliction they had endured. What was the cause of the affliction? From my research the region had suffered ravages of civil war between Caesar and Pompey.
Despite this their abundant liberality or generosity matched their joy. In short, they gave out of their poverty. Remember the widow at Mark 12:43,44. Also notice what Paul says at 2 Corinthians 8:12, "For if the readiness is present, it is acceptable according to what a man has, not according to what he does not have."
Because they were saved the Apostle Paul was surprised that their offering was beyond anything He could have hoped for. (vs5). First, they gave themselves in full devotion to the Lord. Giving of money to God apart and from that would be pointless. We are saved first, (Ephesians 2:8-10) and good works justify our salvation. So, from what I can see Nigel in your comment, you answered your own question.