First - Lactose intolerance is NOT an allergy.
Almost all humans produce lactase (the enzyme that breaks down lactose in milk) when they are babies, but generally lose this ability as they get older and no longer need milk to survive. It is believed that certain European populations retained the ability to produce lactase throughout life via natural selection (those who could drink milk and eat dairy products when there was little else available survived and passed this trait down, while others did not).
The vast majority of people throughout the world are lactose intolerant (see http://anthro.palomar.edu/adapt/adapt_5.htm). Which kinda tells you that consuming dairy might not be a good thing in general. Also, keep in mind that lactose is a sugar, so it's going to make your blood sugar rise.
If you really want to eat dairy, most people who are lactose intolerant find that they can have small amounts of milk products, but can't overdo it. I am lactose intolerant and can have cheese and yogurt without any issue. But if I even see a glass of milk, my stomach starts churning. If I dare to drink it, I'm in the bathroom for a good 30 minutes. Not fun. I love the taste of ice cream, but often find that if I eat more than 70 grams of the stuff, my belly hurts and the gas is just, well, you get the idea.
For me, I just try to avoid any of the dairy products that I know I can't break down (primarily milk and icecream). If I want dairy, I choose things like yogurt. Even frozen yogurt is usually OK for me in small quantities. If you keep portions small, you may find that symptoms are minimal. I know some folks take lactaid, but to me, if I my body can't digest it, that's my body's way of telling me NOT to eat it.