Flatten tenderloins to 3/4-in. thickness. In a large resealable plastic bag, combine the oil, sherry or broth, soy sauce, lemon juice, onion, ginger and pepper; add the turkey. Seal bag and turn to coat; refrigerate for at least 3 hours, turning occasionally.
If grilling the turkey, coat grill rack with nonstick cooking spray before starting the grill. Drain and discard marinade. Grill turkey, uncovered, over medium heat or broil 4 inches from the heat for 4-5 minutes on each side or until juices run clear. Serve on buns with onion, tomato and lettuce.