This is hardly an antinomian life. The Heidelberg Catechism, with its guilt-grace-gratitude framework, introduces the Ten Commandments as the way to exemplify a life thankful for God's gracious salvation. And that's how it works, too, in the New Testament; the apostolic imperatives are always founded upon who the believer is on account of what God has already done in making him a new creation. (Yes, the law is for lawbreakers, to silence them and fell their pride, but the law also functions in a new way for those who are redeemed and forgiven in Christ.) But as we trust our Father's goodness, his statutes for our life bring his blessings to us, and we are drawn deeper into our relationship with him. We thus feel more sure of his mercy and more free to come to him in need. Free grace does not undo the law, but rather brings out its real purpose in our lives: drawing men to God, who give glory to their Maker and Savior by honoring, trusting in, and delighting in him.
I hope this clears up what a life of gratitude looks like, one in which reciprocal love is in view but "payback" is not.