In a bowl, combine lime juice with jam and chile.
Heat 1 Tbsp oil in a large skillet on medium-high. Add onion and red pepper, season with ¼ tsp each salt and pepper, and cook, tossing occasionally until tender, 8 minutes. Add garlic and cook, tossing 1 minute. Transfer vegetables to another bowl.
Return the skillet to heat and add remaining Tbsp oil. Season chicken with ¼ tsp each salt and pepper and cook, tossing once, until browned, 4 minutes. Toss with jam mixture; cook 1 minute.
Return vegetables to the skillet and toss. Spoon into lettuce leaves and top with cilantro.