Sprinkle chicken with salt and lemon pepper.

Heat oil in a large skillet over medium heat. Cook chicken breasts until no longer pink in the center and the juices run clear, 13 to 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove and keep warm.

Place bacon in a large skillet and cook over medium-high heat, turning occasionally until evenly browned, about 10 minutes. Transfer bacon slices to a paper-towel-lined plate. Reserve 2 tablespoons drippings in the skillet. Add onion and brown sugar and cook, stirring occasionally until onion is golden, about 5 minutes.

Place two bacon strips on each chicken breast half, top with caramelized onions, and sprinkle with Colby-Monterey Jack cheese.