What does it mean that the believers first gave themselves to the Lord?
It means the believers first committed themselves to the Lord by stepping into God's saving grace, and only afterward opened themselves to the Apostle Paul and his ministry. Their giving followed a prior surrender to God, not a legal rule, but grace-led generosity as the Lord prospered and laid it on their hearts.
Les explains that this giving was not under any legal binding or set of rules and regulations. The saints were to give as God had prospered them and as the Lord laid it on their heart. But before that, they gave themselves first to the Lord—in other words, they stepped into God's saving grace—and then they might open themselves up to the Apostle Paul and his ministry. Titus was then to finish the same grace among them, gathering offerings for the poor saints.
And this they did, not as we hoped, but first gave their own selves to the Lord, and unto us by the will of God.