In a large plastic bag that is resealable, combine the lemon juice, oil, garlic and thyme. Add the tuna and then seal the bag and turn to coat. Refrigerate for up to 30 minutes, turning occasionally.
Remove tuna from bag; sprinkle with salt and pepper. Drain and discard marinade. Moisten a paper towel with cooking oil; using long-handled tongs, lightly coat the grill rack.
Grill tuna, covered, over medium-hot heat or broil 4 inches from the heat for 3-4 minutes on each side for medium-rare or until slightly pink in the center.
