Drain the tofu, and then remove excess moisture by cutting it in half lengthwise and microwaving on high, uncovered, for two minutes. Gently squeeze out and wipe off excess moisture, then throw tofu in the freezer for one or two hours before removing to thaw in the fridge -- this will give the tofu a slightly heavier texture.
Cut tofu into tiny cubes (about 1/4" thick) and arrange in a lidded dish to be marinaded. Combine brown sugar, soy sauce and rice vinegar in a small bowl. Pour over tofu. Let sit in the refrigerator for at least an hour; I usually leave it overnight.
Heat olive oil in a skillet over medium-high heat. Add tofu, water chestnuts, mushrooms, onion, and garlic and cook until vegetables are tender.
Dissolve 1 Tsp brown sugar in 1 Tsp soy sauce and add to pan. Saute until well mixed and heated through. Spoon mixture into lettuce leaf "bowls".
For the sauce, combine sugar, water, soy sauce, rice vinegar, ketchup, lemon juice, sesame oil, mustard and garlic in a bowl; pour over lettuce wraps and serve.