Preheat a grill for medium heat (350° to 450°). Put bell pepper, mint, lemon juice, garlic, cayenne, 1 tsp. pepper, and 1/2 tsp. salt into a food processor and pulse just until coarsely chopped. Set chutney aside.
In a medium bowl, combine lamb, cilantro, remaining 1 tsp. pepper and 1/2 tsp. salt, the coriander, and cumin until blended. Form into 4 patties, each about 1/2 in. thick.
Lightly oil grill and cook burgers, turning once, until done the way you like, about 6 minutes total for medium. Cut burgers in half and put 2 halves into each pita piece, then tuck in lettuce leaves. Serve chutney on the side.
Note: Nutritional analysis is per serving.