Is all lactose-free milk sweet?
When making lactose free milk, the lactose isn't actually removed. Instead, lactase is added to the milk. This breaks down the lactose into its component sugars, glucose and galactose. Lactose is one of the least sweet sugars, relative to sucrose (table sugar). Both glucose and galactose are significantly sweeter than the original lactose, hence why lactose free milk tastes much sweeter.

Here is a chart showing the sweetness of different sugars.
Video and description of process of making lactose-free milk.