Heat gas or charcoal grill. In large bowl, mix ground beef and salt. Shape mixture into 12 thin patties, each about 4 inches in diameter.
In small bowl, mix pepperoni, olives and 1/3 cup of the pizza sauce. Spoon rounded tablespoon pepperoni mixture onto center of 6 patties; spread slightly. Top with remaining patties; press edges together firmly to seal.
Place patties on grill; cover grill. Cook with medium heat 8 to 12 minutes, turning once, until thermometer inserted in center of patties reads 160°F (avoid inserting in filling). During last 1 to 2 minutes of cooking time, top each patty with cheese and rounded teaspoon of remaining pizza sauce, and place buns, cut side down, on grill; cook until cheese is melted and buns are lightly toasted.
To serve, place lettuce and patties in bottom halves of buns. Cover with top halves of buns.