That is my understanding as well. Once a person has been on the gluten free diet for some time- say about 6 months, the villi do start to repair themselves. This is why, for many, the lactose intolerance is temporary.
Personally, I could tolerate very little dairy at first, but am now able to eat most dairy- I still avoid large glasses of milk, and sometimes get uncomfortable after eating ice cream, but I refuse to avoid it for that reason

Of course, milk allergy and lactose intolerance are two different things, and it IS possible to have both. If the symptoms persist, or do not respond to the lactaid or lactose-reduced dairy products, it is wise to have the testing done as Sharon described. If you have an allergy to casein, the problem is not related to the damaged villi, and it is wise to continue avoiding dairy.
Some people just naturally produce less lactase (the enzyme needed to digest lactose) and even as their villi return to normal, lactose intolerance can persist, but in that case, lactaid would generally help. This is commonly seen, for instance, in people of Asian heritage.
I hope this answers your questions