May be not directly the lactase, but the split' lactose. Lactose is split into (milk) sugar by lactase enzyme. Lacto-free milk is sweeter than whole milk. So, it's the same problem with as with all sugars.

the lactose is converted in glucose, so probably yes, but it depends on the original quantity of lactose

Lactase splits the lactose into glucose and galactose, so they would get more fast sugars and would need to consider that in their sugar intake.