Break the lettuce into piece to lay flat, layer 3/4 inch in the bottom of 11"x13"x2" cake pan (preferably glass).
Sprinkle the red onion and celery over top, then sugar and the peas (previously cooked and chilled).
Spread a layer of mayo over the top, just so the peas are covered, touching all sides. Sprinkle the bacon or bacon substitute and finish with a layer or parmesan (the more, the better).
Refrigerate at least 8 hours. Serve chilled.