In a large resealable plastic bag, combine the first seven ingredients. Add pork; seal bag and turn to coat. Refrigerate 8 hours or overnight.
Drain pork, discarding marinade. Moisten a paper towel with cooking oil; using long-handled tongs, rub on grill rack to coat lightly. Grill pork, covered, over indirect medium heat for 25-40 minutes or until a thermometer reads 145°. Let stand for 5 minutes before slicing.
In a small bowl, combine the mayonnaise, sour cream, lemon juice, sugar, ground mustard, Dijon mustard and horseradish. Serve pork on rolls with lettuce and mustard horseradish sauce.