Prepare the vegetable papillote according to package instructions.
Place the papillote on the barbecue grill or in the oven and cook for 12 to 15 minutes.
Baste the lettuce with a little bit of oil and season. Grill the lettuce quarters quickly.
Mix the remaining olive oil with the lemon juice and dill.
In a serving dish, place the grilled lettuce quarters, add the contents of the papillote and drizzle with the dressing. Season to taste and serve with grilled meat or fish.