Sometime New Orleans resident Daniel Lanois is one of the world’s most sought after producers—so busy, in fact, that he rarely finds time to work at his French Quarter studio. Yet he wants to be recognized as a recording artist in his own right. His second album—and new, lean band of locals—should go a long way toward achieving that goal.

On a fine early-spring Saturday afternoon in New Orleans, the streets of the French Quarter are alive with merriment. But the occupants of a three-vehi...