This is when Uber should go back to their investors, ask for $10B and just buy Lyft.
Without Lyft Uber will have an easier time to become profitable and avoid a "race to zero" in cities when they compete against each other.
I also think that people overestimate the effect that Lyft per se has on Uber's prices/margins. Uber competes not just with Lyft, but with other, smaller "use an app to get a ride" apps, and with taxis, public transit, using your own car, and not going to where you're going. Even if Lyft rolled up its operations tomorrow, I don't think you'd see more than a marginal effect on Uber's unit-profit/volume tradeoffs.
I'd heard, anecdotally, that many (most?) Lyft drivers also drive for Uber.
That's also why they'd have to pay a large premium over the current $7.5B valuation, such as the $10B suggested by parent.
I'm unaware of any transportation companies that could really afford to purchase Lyft.
I always make a point of asking the driver if they work for both and my informal polling has been overwhelmingly "yes" on the question of "do you work for both?"
I've been on rides before where, a few blocks from my destination, the driver will open up the opposite app to start polling for a new rider before even dropping me off.
You can browse all anti-trust cases here:
https://www.justice.gov/atr/antitrust-case-filings?page=1
Here's a typical example, that is a million miles away from something like the Microsoft case:
Even though they wouldn't be a monopoly, it wouldn't be hard to argue that merging Uber and Lyft would substantially lessen competition.
Size-wise, especially in some locations Uber and Lyft now dwarf the regular taxi services. So you're probably right that this would at least be reviewed and likely flagged down, assuming that such local issues would be enough to raise that flag.