Heat a large frying pan over medium-high heat. Add grapeseed oil, turkey, and onion; fry for 5 minutes. Add sliced mushrooms and garlic. Cook until turkey is browned, 5 to 10 minutes more.
Reduce heat to medium-low. Add chili, cumin, paprika, salt, thyme, and pepper; stir for 1 minute. Add beans, ketchup, Worcestershire sauce, and soy sauce. Cook and stir for 5 minutes.
Spoon turkey mixture into lettuce leaves. Top with chopped mushrooms, bell pepper, tomato, and green onions.