Coat a small nonstick skillet with cooking spray; place over medium heat until hot. Add onion; saute 5 minutes or until tender. Remove from heat; let cool. Combine onion, beef, breadcrumbs, water, and egg white in a large bowl; stir well. Divide mixture into 8 equal portions, shaping into 1/2-inch-thick patties. Spoon 1 tablespoon cheese into the center of 4 patties; top with remaining patties. Press edges together to seal.
Prepare grill. Place patties on grill rack coated with cooking spray; grill 4 minutes on each side or until done.
Spread 1 tablespoon sour cream over top half of each muffin, and set aside. Line bottom halves of muffins with lettuce leaves; top each with a tomato slice,a patty, and top half of muffin.