Iain Mathieson, a Harvard scientist and the lead author of a recent peprint on the history of natural selection in Europe, has a website where he occasionally posts articles. He recently posted a review on the origins and spread of lactase persistence (LP) in Europe. He ends the review with the following comment:
This is actually rather consistent with the Itan et al. result, and it seems plausible to me that the [European LP] allele first appeared in Central Europe, was spread around Europe by the LBK, before being introduced to the steppe later by migration from Europe.
I can imagine that this conclusion won't be everyone's cup of tea, but I'd say it's a reasonable one for the time being.
Also, it's interesting to see the presence of the European LP allele in the Srubnaya Culture remains from the Middle Bronze Age Caspian steppe.
We didn’t find any evidence for LP in early farming populations like the LBK, or in early Bronze age steppe populations like the Yamnaya. In as-yet unreported data, we find a few copies of the allele in the Srubnaya - a later steppe population who seem to have some European Farmer-like ancestry.
The same Srubnaya sample also shows a high ratio of Y-haplogroup R1a-Z93 (4/6), which is today one of the most common Y-haplogroups in South Asia.
Now, the LP allele in South Asia is the same one as in Europe. So what this suggests is that at some point, probably during the later stages of the Bronze Age, steppe nomads closely related to the Srubnaya people moved into South Asia, bringing with them both R1a-Z93 and the European LP allele.
I'm pretty sure we'll be hearing more on that soon from the good people at Broad MIT/Harvard.