In a food processor, process garlic scapes with lemon juice, salt and pepper until finely chopped. Add cannellini beans and process to a rough purée.
With motor running, slowly drizzle olive oil through feed tube and process until fairly smooth. Pulse in 2 or 3 tablespoons water, or more, until mixture is the consistency of a dip. Add more salt, pepper and/or lemon juice to taste.