If the beans are fresh, cook them in salted water until they are soft. Also cook the potatoes until tender.
Drain the water from the pot and mash the potatoes with some of the whole milk to a creamy mass. Mix the buttermilk with the rest of the whole milk and flour and then add the mixture to the potato mixture, ideally with a whisk.
Drain the beans and add. Bring everything to the boil and season with lemon juice and salt.