Press tofu between paper towels or in a tofu press, for 10-15 minutes to remove excess moisture, then crumble into small pieces.
Heat oil in a large skillet over medium-high heat. Add diced onion, garlic, ginger, and white parts of green onions. Sauté for 2-3 minutes until softened and fragrant.
Add crumbled tofu to the skillet and cook for 5-7 minutes, stirring occasionally, until tofu is golden brown and crispy.
Stir in water chestnuts, soy sauce, vegan oyster or hoisin sauce, and sambal chili paste if using. Cook for 2-3 minutes until heated through and well combined.
Remove from heat and garnish with green parts of green onions.
Serve immediately with lettuce leaves, allowing guests to scoop filling into lettuce cups and wrap.