I learned about it on a BBC documentary about the Black Death I saw a few years back. I'm about to run out the door so I haven't the time to properly figure out which one and see what paper they were citing. But I remember it was a French university that did the genetic tests, IIRC.

The data which fit that theory better came from London and some city in Scotland (Glasgow? I'm not sure.) Basically there were houses which shared gardens (where rats would live) but the disease didn't spread between the two houses. Likewise in London there was a poor district that got hit hard, and a rich district next door that saw very few infections. Due to the way the sewers were laid out, the rat population was the same between the two. But the lice wouldn't have transferred without close contact, which of course rarely happened between rich and poor.

The more damning evidence was out of Scotland where the doctor making a very detailed study showed that the disease only transferred between people who shared close living quarters. And in particular, during a lockdown with all-day curfew it didn't transmit at all. But where beds were reused, the new inhabitants got sick.

But the genetic evidence sealed the deal. I'll have to look up that French study later.

A paper on the modeling which shows that Black Death was probably spread by lice, not rats:

https://www.pnas.org/doi/10.1073/pnas.1715640115

And a news article presenting an interesting overview about various research on the causative agent for Black Death, including genetic studies:

https://www.nbcnews.com/id/wbna44489863

I couldn't find any genetic studies showing that lice was the vector for spread, so maybe I was misremembering or conflating the two points.