Heat oil in large skillet over medium-high heat. Add lemongrass and garlic; sauté 2 minutes. Add mushrooms. Sprinkle with 1/2 teaspoon coarse salt; sauté until mushrooms are tender, about 4 minutes. Remove from heat; cool in skillet.
Place pork in large bowl. Mix in 1 tablespoon soy sauce, 1 teaspoon sesame oil, cracked pepper, and 1/2 teaspoon coarse salt, then fold in mushroom mixture. Using 2 generous tablespoonfuls for each, shape into 18 patties, each about 2 1/4 inches in diameter; arrange on plastic-lined baking sheet.
Whisk hoisin sauce, ginger, vinegar, chili sauce, and remaining 1 tablespoon soy sauce and 2 teaspoons sesame oil in small bowl for sauce. DO AHEAD: Burgers and sauce can be made 6 hours ahead. Cover separately; chill.
Spray grill rack with nonstick spray. Prepare barbecue (medium-high heat ). Grill burgers until cooked through, about 3 minutes per side. Arrange burgers on platter; set out sauce. Place lettuce, bell pepper, carrot, and cilantro in separate bowls. Serve, allowing guests to wrap burgers in lettuce and add sauce and vegetables as desired.