Sprinkle chicken with salt and lemon-pepper. In a large skillet, cook chicken in oil for 13-15 minutes or until juices run clear; remove and keep warm.
In the same skillet, cook bacon over medium heat until crisp. Using a slotted spoon, remove to paper towels; drain, reserving 2 tablespoons drippings. In the drippings, saute the onion and brown sugar until onion is golden. Place two bacon strips on each chicken breast half; top with caramelized onions and cheese.