Lactose is a complex sugar made of two simple sugars.
Lactose free milk is for lactose intolerant people who don't have the enzyme to break down the lactose molecule into it's two pieces. That is a stomach enzyme called lactase. So, the lactose free milk has that enzyme (Lactase) added to the milk. So instead of drinking milk with lactose, they are drinking milk with the lactose split in two sugars that it's made of: glucose + galactose.
So no, it has exactly the same amount of sugar.