Heat oil in a heavy skillet or wok over medium-high heat. Add shallot and cook until softened, about 2 minutes, then add ginger, garlic, chile and lime leaves and cook until fragrant, about 1 minute more. Stir in pork and beef, and cook, breaking meat up into small bits with spoon and stirring occasionally, until cooked through.
Add brown sugar and continue cooking, stirring frequently, until meat is browned and crispy, about 10 minutes more. Stir in lime juice, herbs and fish sauce. Add salt to taste.
Stir together sweet chili and sambal oelek. Transfer meat to a bowl and allow guests to build their own lettuce wraps, with lettuce leaves, shredded carrots, herbs and sauce.