Boil 2 cups water, brown sugar, lemon juice, juiced lemon halves, and apple together in a pot over medium-high heat until apples are tender, 10 to 12 minutes. Discard spent lemon halves; drain and keep apples warm.
Boil potatoes with 6 cups water in a large pot over medium-high heat until tender, 15 to 20 minutes. Drain.
Mash potatoes and apples together with a ricer or hand mixer.
Stir butter, heavy whipping cream, salt, and ground black pepper into mashed potatoes and apples. If desired, keep warm in a 350 degrees F (175 degrees C) oven for up to 20 minutes.