Shred tuna into a large bowl. Stir in carrots, olives, and red onion. Stir until evenly distributed. Add salad dressing until moist enough to hold together.
Slice hoagie rolls in half horizontally and spread each with 1 tablespoon Dijon mustard. Top rolls with lettuce and divide tuna mixture between the 2 rolls. Replace roll tops and slice each hoagie in half to make 4 sandwiches. Makes 4 servings.