To prepare lemon mayonnaise, combine 1/4 cup mayonnnaise, chives, 1 teaspoon lemon juice, and 1/8 teaspoon black pepper; stir well.
Combine lemon mayonnaise, tomato, and lobster; stir well. Divide the lobster mixture evenly among flatbreads. Top each serving with 2 lettuce leaves. Roll up jelly-roll fashion.