Season the chicken breasts on both sides with salt and lemon pepper. Heat ½ tablespoon of the oil in a medium-sized skillet and brown the chicken breasts on both sides, about 3 minutes on each side. Transfer to a plate.
In the same skillet, add the other ½ tablespoon of oil and saute the onions until translucent. Add the real bacon bits.
Sprinkle the brown sugar over the onion/bacon mixture and add the whipping cream. Cook for a couple of minutes until the sugar has melted and the sauce is heated through. At this time check for seasoning and adjust adding salt and pepper.
Return the chicken breasts to the skillet, top with the onion/bacon mixture, and distribute the shredded cheddar cheese evenly among them. Cover the skillet with the lid, reduce the heat to low, and simmer for about 10 minutes.