I switched to mainly water quite awhile ago and they never ask for it. (Milk I mean lol) The odd time I'll give them choc milk for a treat or if we eat at a restaurant. We eat a lot of dairy so I felt it wasn't needed and I was dumping a lot of milk out at end of day
As to your question....I fill up their cups every morning and only refill as needed so if they had milk leftover at lunch, yes they'd get it at next snack