Lactose intolerance is completely different from being allergic to milk products, people who are allergic to milk products are allergic to the casein in milk products, people that are lactose intolerant are intolerant to the natural sugar (lactase) in milk products.
I was lactose intolerant as a baby, but was fine in my toddler yrs and all the way through until I hit 35 yrs old and then became intolerant again...I got sick with crohn's at 23 just before turning 24, so I was sick with CD for a long time before becomming lactose intolerant again, and it sucked because I didn't even realize I had become lactose intolerant since the symptoms of it were easily masked by the symptoms of my crohn's....my GI just happen to test me for it when I was 36 (I'm 41 now) and sure enough, it was discovered that I had a severe lactose intolerance.
I used lactaid products with success, then I discovered a particular probiotic that actually aids with lactose intolerance issues (as well as high cholesterol and for women, vaginal health but it's still fine for men to take this probiotic of course) and shortly after I started using this particular probiotic, I tested it out and found I no longer had to use lactaid products anymore.
Lactose intolerance is pretty common, I think it's estimated that something like 75% of the population is lactose intolerant to some degree (there's mild, moderate and severe degrees), and it is very common for IBDers to have issues with lactose intolerance, too bad IBD wasn't as easy to deal with like lactose intolerance is.