First off, note that UberLawyer was registered a few years before Uber existed.
The word uber itself has a meaning of "denoting an outstanding or supreme example of a particular kind of person or thing."
Therefore UberLawyer would be recognized on its own as non-infringing and legitimate domain and no problem at all using it as a lawyer's website.
However, since they specifically call out Uber & Lyft & ridesharing in general, obviously that's where Uber could make a complaint.
From a domain dispute perspective, I'd think their current usage is at least inviting a dispute. But the complainant has to show bad faith:
(i) the domain was registered primarily for the purpose of selling it to the complainant or a competitor for more than the documented out-of-pocket expenses related to the name; or
(ii) the domain was registered in order to prevent the mark owner from using it, provided that the registrant has engaged in a pattern of such registration; or
(iii) the domain was registered primarily to disrupt the business of a competitor; or
(iv) by using the domain, the registrant has intentionally attempted to attract users for commercial gain by creating a likelihood of confusion as to source or affiliation.
But I'd see it panning out like this:
(i) fail. Registered prior to Uber's existence by a few years.
(ii) fail. Registered prior to Uber's existence by a few years.
(iii) fail. They're not a competitor.
(iv) probably fail. I don't anyone is going to think they're hiring a lawyer that works for uber when they're trying to sue uber over an accident.
So I kinda think they might win the dispute (but you never really know...).