Cook the floury potatoes in plenty of water over medium-high heat for 20-30 minutes, depending on your preferred texture.
While the potatoes cook, peel and quarter the apples and remove the cores. Place them in a saucepan with some water, the 1 tablespoon sugar, and the squirt of lemon juice. Cover and simmer over medium heat for about 15-20 minutes, stirring every 2-3 minutes.
When the potatoes are tender, drain and peel them, then return them to the pot. Mash the potatoes thoroughly with a potato masher. Mash the cooked apples and add them to the potatoes. Stir in the dash of milk and some butter. Season to taste with salt, pepper, and a pinch of nutmeg. Taste and add more lemon juice if desired. Stir vigorously until well combined.