And perhaps Uber has some heuristics (ancient English for AI) or competitor intelligence to detect if a driver has accepted a Lyft ride. Uber can then offer a carrot to that driver to get them to cancel the Lyft ride. They could offer the best fare that turns up in the next 2 minutes. Costs Uber little, causes three damages to Lyft (Lyft lost profit, annoyed Lyft customer, driver happier with Uber).
Yes, I wouldn't be surprised at all if they have ways to do that and micro target better rates on fares that have a pending Lyft pickup.
Remember on the driver side they run on different phones generally, but on the client side the customer is running all these apps on their single phone. A lot of these apps have privacy issues and snoop a lot on the client side. So they can basically detect frequency/recency of Lyft app being open on your phone, and then offer Uber drivers better rates for pickups at your GPS location.