In a 3-quart saucepan bring broth to a boil, and add 2 cups peas and cook, stirring occasionally, until tender, about 4 minutes.
Using an immersion blender or standing blender, puree mixture until smooth (use caution when blending hot liquids. Add the mint and butter and blend until smooth. (If using a standard blender return the sauce to the saucepan.) Strain the sauce. Add the remaining 1/4 cup peas and simmer until peas are just tender, about 2 minutes. Season sauce with salt and pepper and add lemon juice, to taste. Serve hot or at room temperature.