First, why is everyone saying DIARY ??
I'm lactose intolerant. After the age when people really need milk, the body stops producing lactase, the enzyme needed to digest lactose. However, people who continue drinking milk regularly even as adults, find that their bodies continue to produce lactase. There are also some genetic factors to it. At a certain point i stopped consuming even small quantities of milk (i dont do tea/coffee), and soon i was lactose intolerant. I can still have very small quantities of milk without issues, ice cream is not an issue and neither is dahi/yoghurt. But if i go to a decent place and have a milkshake or even a rich cold coffee, i'm screwed. Watery cold coffee is still doable.
Most ice creams rarely use real cream (Information Courtesy Amul). Anway, cream has very little lactose in it. Similarly yogurt also has very little lactose as the bacteria multiply by consuming the carbs (lactose). Cheese too has very little lactose as most of it is separated as whey. Aged cheeses have the least amount of lactose. Milkshakes and Cold coffee obviously has milk which has loads of lactose.