As to the connection between Tregs and lactate, I don't think this has been established yet. It could be that in non-balding people, the regular appearance of Treg cells around the follicle send signals to regulate lactate dehodryogenase enzyme, which then activates the stem cells to proliferate and differentiate. What we're looking at here is a multi-staged cycle with a lot of different steps.
The whole thing about lactate and pyruvate makes a lot of sense to me, though. Hair follicle growth requires a tremendous amount of concentrated energy. The UCLA research indicates that in normal skin cells, pyruvate gets shunted towards the mitochondria to create energy for the cells, but this doesn't happen in hair follicle stem cells. In HFSCs, the "fuel" turns out to be lactate (also known as lactic acid). Interestingly, in striated muscle cells, after exercise, you make a lot of lactic acid, which causes muscle fatigue. It kind of makes sense to me, on a deep level, that the signaling for hair growth might involve lactate. The body compartmentalizes its functions, and a chemical that in one part of the body has one effect, might have a completely different effect in another part of the body. In your scalp, you have almost no striated muscle fibers, because people can't move their scalps at will. So, it makes sense that lactic acid could have a completely different function there.