Place diced bacon in a large, heavy skillet and cook over medium-low heat until all the fat is rendered and bacon bits are very crisp, about 15 to 20 minutes.
Remove bacon with a slotted spoon, drain on a paper towel and reserve.
Add diced red onion to skillet and cook over medium heat until very soft, about 5 to 7 minutes.
Sprinkle sugar evenly over onions and cook over low heat, without stirring, until the sugar caramelizes, about 10 to 15 minutes.
Cool completely, then fold into mayonnaise.
Put a lettuce leaf on each of 4 serving plates.
Put 2 tomato slices to one side on each plate.
Spoon chilled dressing over lettuce.
Pour clarified butter or oil into a large heavy skillet and heat over a medium flame.
Dredge 4 soft-shell crabs in seasoned flour, shaking off excess, and place in skillet.
Cook 2 to 3 minutes per side (jumbos will take longer), until crisp.
Hold in a warm place while cooking remaining crabs.
Transfer to prepared plates and sprinkle with reserved bacon bits.