Sprinkle tuna with lime juice, salt and pepper. Moisten a paper towel with cooking oil; using long-handled tongs, lightly coat the grill rack. For medium-rare, grill tuna, covered, over high heat or broil 3-4 in. from the heat for 3-4 minutes on each side or until slightly pink in the center. Cut into 1-in. pieces.
Finely chop the celery, peppers and onion; place in a large bowl. Add the torn lettuce, tuna, basil and rosemary; toss to combine.
Arrange lettuce leaves on four plates; top each with 2 cups tuna mixture. Drizzle with dressing.