"Keep my decrees and laws, for the man who obeys them will live by them. I am the LORD."
What does it mean when God says "I am the LORD" and why is it used as a basis of command? The LORD is good, kind, gracious, compassionate, slow to anger and abounding in steadfast love. (Ex 34:6-7) On this basis God establishes his authority to command. Because of his divine character, we can trust in his judgment. Because of who he is, we can delight in his laws. We know they are for our good because we know who God is by who he has revealed himself as in the person of Jesus Christ (Col 1:15).
And those who obey will live by the commandments. The meaning is twofold: that they will both live in accordance with the Law and that it is obedience to God which brings life. Jesus completely agrees as well. The New Testament does not abolish the Law so that we can pretend it no longer applies. Rather Christ fulfills the Law (Rom 8:3-4) and does away with the curse by becoming a curse for us (Gal 3:13), but we still must obey Christ for the man who obeys will live.
Grace does not do away with the necessity of obedience but rather the curses of disobedience. However, obedience comes only through faith and the empowerment of the Holy Spirit who guides us and reminds us of all that Christ taught. Those who try to obey on their own strength of will are subject to the curses (Gal 3:3-10), but those who are righteous by faith will live. (Rom 1:17)