Mix the mayonnaise with the shallot, mustard, tomato puree , tarragon, tabasco to taste and salt and pepper. Stir about three quarters into the crab. Taste and add the rest if it needs it- the mixture should be quite sloppy. Check seasoning.
Just before serving shred the lettuce leaves and toss with the vinaigrette. Divide between individual bowls or plates then top with the crab mayonnaise.
Serve with lemon wedges and brown bread and butter or toast.