Sprinkle chicken with salt and lemon-pepper. In a large skillet, cook chicken in oil for 6–7 minutes on each side or until a meat thermometer reads 170 degrees; remove and keep warm.
In 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, sauté onion and brown sugar until onion is tender and golden brown. Place two bacon strips on each chicken breast half; top with caramelized onions and cheese.
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