Yeah, I think Colaly is right. I think the "live and active" is just an ad man's phrase to inspire more sales.
In reality, all "live and active" yogurt cultures are probiotics. If you look at a container of probiotic capsules, they contain many of the same cultures as are contained in yogurt. I've really only read the probiotics labels for animal use (DON'T try to use these for humans, please, as they can make people pretty sick), but they contain some common ingredients.
The reason they help with lactose digestion is because they form the enzyme lactase, which is lacking in the systems of most adult humans. Lactase digests lactose. If it doesn't get digested properly it can cause problems.
I've solved that issue for myself by drinking raw milk from my healthy cow.