Place the crab in a bowl and run your fingers through it to check for pieces of shell. Break up the crab a bit with your fingertips, but leave several large pieces. Add the chili sauce, lemon zest and juice, parsley, hot sauce and Worcestershire sauce to the bowl and toss to combine.
In a food processor, process the chopped veggies into small bits by hitting pulse several times. Line a plate with a few sheets of paper towel. Scrape the veggies onto the towel to remove the liquids.
Transfer the chopped celery, pepper, garlic and onions to the crab. Stir to combine the veggies and season the salad with coarse salt and pepper, to taste.
Place the crab salad in a serving bowl and top with the crackers. Surround the salad with lettuce “cups.” Spoon the salad into the crunchy pieces of lettuce as you eat.