Cook onion mixture and garlic in 2 tablespoons butter in a 4- to 5-quart heavy pot over moderately low heat, stirring, until softened, 3 to 5 minutes. Add coriander, salt, and pepper and cook, stirring, 1 minute. Stir in potato, lettuce, and water and bring to a boil, then reduce heat and simmer, covered, until potato is very tender, about 10 minutes.
Purée soup in batches in a blender (use caution when blending hot liquids) and transfer to a 2- to 3-quart saucepan. Bring soup to a simmer, then whisk in remaining tablespoon butter and salt and pepper to taste.