We drink Milk Kefir (not Water Kefir) everyday - actually mostly I make my Kefir from Soy Milk, periodically mixing with real milk.
So, if you milk intolerant - you can start on Fermented Soy Milk or any other Milk substitute such as Nut or Seed Milk.
However, Real Milk should be OK too - since Kefir Grains will Ferment Lactose in Milk and it will be safe for you to drink. Just keep the fermentation a bit longer to make sure all the lactose is fermented.
My husband has type II Diabetes - I give him Kefir everyday without any problems... it helps cure Diabetes.
Actually, we already reversed his diabetes and i give him Kefir for general well-being.
We cured many health problems with Kefir.
You can do search on internet about benefits of Kefir.
Your digestion will improve greatly on Milk Kefir!
Your food intolerance will disappear!