In a resealable plastic bag, combine the lemon juice, oil and pepper; add turkey. Seal bag and turn to coat; refrigerate for up to 2 hours.
In a small saucepan, combine the vinegar, wine or broth and tarragon. Bring to a boil; cook until reduced by half. Reduce heat; add butter and mustard. Stir until butter is melted; set aside and keep warm.
Drain and discard marinade. Grill turkey, uncovered, over medium heat for 5 minutes; turn and baste with mustard sauce. Cook 10-15 minutes longer or until juices run clear, basting frequently.