Yes, lactose tolerance is autosomal and could easily decouple from Y or Mt DNA of its original carriers. It flowed freely through populations following spread of domesticated cows, or other words the best climatic conditions for herding them. In far past central Asia was moist and green with best conditions for herding. Since 5-4 thousand years ago it started to dry out, at the same time central Europe became mild and moist with rich grass cover, creating the best conditions for herding. For that reason lactose tolerance turned to be a great benefit to the people of central Europe and had spread to over 90% of population in this region. Regardless of paternal and maternal chromosomes.
Interesting example, though in reverse, is how R1b people went to central Africa, few thousands years ago, and completely lost white skin color. Obviously, there was no benefit of having white skin there in tropics. Possibly rampant skin cancer and vitamin D overdose.