Mix first 4 ingredients in large bowl until blended. Shape into 4 balls. Poke deep hole in each ball and fill each with 1 1/2 tablespoons of cheese. Mold meat around cheese to enclose. Flatten each filled burger to 3/4-inch-thick patty. (Can be made 8 hours ahead, covered and chilled.)
Grill burgers to desired doneness, about 5 minutes per side for medium.
Place burgers on bottom halves of buns. Top with lettuce, tomatoes, onions and upper halves of buns.