Heat a grill to medium heat.
In a small bowl, whisk together lemon juice, olive oil, shallot, vinegar, garlic, and a pinch of salt and pepper.
Slice lettuce heads into four parts and brush olive oil onto the cut side. Season with salt and pepper.
Grill lettuce, cut side down, until lightly charred, about 2 minutes.
Remove from grill and place on a plate. Add cherry tomatoes and drizzle marinade over lettuce; season with another pinch of salt and pepper and garnish with torn parsley.