I've seen conflicting reports about this.

We know the age of the mutation to correspond with the timeline of the PIE invasion of Central Europe. We know it is one of the few haplogroup G2a clades to be found in Scandinavia. It very clearly appears to be tied to the PIE invasion and very clearly appears as if the Halstatt culture had quite a few G2a3b1a men who were in the first Italic tribes to cross the Alps and become the Romans along with the R1b's. They most likely would be indistinguishable phenotypically from the R1b's.

Many people consider G2a3b1a to be the PIE branch of the G family.

However, what is not clear to me is whether or not G-L497 was part of the LBK culture and got assimilated by R1b's somewhere near the Alps and then became the Halstatt Celts or if G-L497 was a clade of G that existed near the PIE homeland having drifted north from their own haplogroup G homeland in the Caucasus or Eastern Anatolia.

Where is the homeland of G2a3b1a?

Also, what is the word on G2a3b1a and lactose persistence? I know that Neolithic G2a's did not have the lactose persistence gene. What do we know about whether or not these "PIE G2a's" had lactose persistence?