Does it?
"We lose money on every customer, but we'll make it up in volume" is one of the classic ways to run a business into bankruptcy. Sometimes, taking one's time is the far sounder strategy, even if a hyper-growth competitor is "everywhere" and "dominating" in the eyes of the uninformed public.
In other words, even Lyft's best case scenario would be a huge step down for Uber.
Sooner or later the free money is going to run out and Uber is going to have to stop hemorrhaging nearly a billion dollars every quarter. When that day comes they're not going to have a lot of options to stop the bleeding: raising prices and cutting back the markets they operate in are likely to be the first things they do, or are forced to do by investors.
Meanwhile, the way you build a huge multinational is by first figuring out a way to make money and then scaling it to everywhere, not by figuring out how to be everywhere and then realizing "crap, we have to actually turn a profit now".
Apparently Uber is already profitable in the US and thus can use that to finance further growth, but nothing is stopping Lyft from going back in that game at a later date. If anything Uber's best strat would probably be to refocus on the US and crush Lyft everywhere, rather than give it the room to breath it needs.
2016 numbers:
Lyft Revenue: $700 million
Lyft Losses: $600 million
Uber Revenue: $6 billion
Uber Losses: $2.8 billion