Greek Yogurt does contain Lactose and so that means that Greek Yogurt is not lactose free.
If you're lactose intolerant then eating Greek Yogurt may cause issues with your lactose intolerance and cause your stomach to hurt.
One 6 ounce serving of Greek Yogurt contains 6.8 grams of lactose so that means that it's pretty high in lactose but some people who are lactose intolerant may be able to eat things such as Greek Yogurt or other Yogurt and even some cheeses and ice cream etc.
But they may have to just avoid milk because milk is higher in lactose than Greek Yogurt, Cheeses etc.
So if you're lactose intolerant you could try a bit of Greek Yogurt and see if it hurts your stomach and if it does then you should avoid the Greek Yogurt.