New elements have come to light since I posted this. Lactase persistence genes have been found among Neolithic populations in Sweden (Funnelbeaker culture and Pitted ware) and Spain (Cardium Pottery) as early as 3000 BCE. The Lactase persistence gene therefore could not have originated in the Steppe, but it isn't certain whether the mutation first appeared among Paleolithic/Mesolithic Europeans or in the Middle East.
Mutations take place completely haphazardly. They don't happen for a reason. So there is no reason to believe that lactose tolerance necessarily originated among milk-drinking animal herders. Actually it is possible that the mutation itself is much much older than domestication, perhaps as much as 20,000 to 50,000 years old. Useless without domesticated cattle or goats the mutation would have stayed dormant and would not have been actively selected for its health benefits until the Neolithic.
If we suddenly see lactase persistence genes pop up in Neolithic Spain and Sweden, in two regions sharing a similar Paleolithic ancestry (Y-haplogroup I + mt-haplogroup U4 and U5) I would be inclined to think that the mutation was already present, even at low frequencies, among most Mesolithic European populations, and that when Neolithic farmers arrived and started to mix with them the selection process started.
If that is the case, lactase persistence gene could have been present in the Mesolithic from Iberia to European Russia, across western, northern and eastern Europe. Thus it could also have been picked up by R1b people once they moved into the Steppe and mixed with indigenous people (mtDNA U4 and U5).
This is the best explanation I have for the fact that lactose tolerance is so much more prevalent nowadays among northern Europeans and especially Scandinavians, who descend heavily from Mesolithic Europeans, and is virtually absent from the Middle East and rare in the Balkans. Since R1b is Middle Eastern in origin but mixed early with northern Europeans in the steppes, then again in central, western and northern Europe, the percentage of people with the lactase persistence gene would have increased as they gradually absorbed indigenous European DNA.