In a 10- by 15-inch rimmed pan, lay bacon slices side by side.
Bake in a 350° oven for 15 minutes. Drain and save fat.
Mix sugar and lemon peel. With your fingers, evenly pat mixture onto bacon slices, covering completely.
Return pan to oven and bake until bacon is well browned, 12 to 15 minutes. With a wide spatula, transfer bacon to a rack; scrape sugar drippings from pan and put on bacon.
Meanwhile, rinse liver, pat dry, and trim off and discard any tough membrane. Cut liver into 4 equal portions.
In a 10- to 12-inch nonstick frying pan, combine onions, lemon juice, and butter. Stir over high heat until onions are limp and slightly browned, about 15 minutes. Add parsley and stir until wilted. Mound onions on an ovenproof platter; arrange bacon in a single layer alongside. Put in a 150° oven. Wipe frying pan clean.
Set frying pan over high heat and add reserved bacon fat. Coat liver with flour, shaking off excess. When fat is hot, add liver. Brown on each side, turning as needed until just barely pink in center (cut to test), about 5 minutes total. Drain liver briefly on towels, then add to platter. Add salt and pepper to taste.