I doubt this killer is in any country except for possibly Mexico. Admittance anywhere else requires a passport, and unless this lawyer of theirs is Saul Goodman, he wouldn’t have had enough time to put together the fake documentation and background to pull it off…
Mexico city has direct flights to Moscow. Russia has no extradition to the USA and doesn’t hold people at their airports just because there is a US warrant for their arrest remember that whole no extradition treaty thing. The USA would have to make a special individual diplomatic request to the FSB to hold a US citizen at the airport. I don’t see the USA asking for a special individual diplomatic request for some wayward boyfriend suspected of a crime.
The way out is overland to Mexico then drive to.Mexico City buy a direct round trip ticket to SVO that’s Moscow’s main airport and walk into Russia in a tourist visa. Then find a crooked type to get you a new ID and a perm res card both are not hard to pay for in the former Soviet Union it is after all a completely corrupt system over there.