In a container with a lid, combine the lemon juice, oil, garlic and thyme. Add the tuna and turn to coat. Refrigerate for up to 30 minutes, turning tuna 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 in. from the heat for 3-4 minutes on each side for medium-rare or until slightly pink in the center.