Remove the stalk from the white cabbage and then grate the cabbage as finely as possible (preferably with a food processor and about the size of rice grains). Peel the carrot and grate it into small pieces. Mix the cabbage, carrots, sugar, salt, pepper, 2 teaspoons of lemon juice and the milk together.
Mix the mayonnaise with buttermilk, 2 teaspoons lemon juice and vinegar well and pour over the coleslaw. Mix everything again vigorously.
Note: It is best to let the coleslaw steep overnight (the Americans even let it steep for 2 days, as this is how the coleslaw tastes best!)
Before serving, season again with salt, pepper and sugar.