Not exactly. The percentage that Lyft takes is the same, so Lyft actually makes more money from these price-hikes. The ones suffering are the passengers.
The existence of other options implies a more elastic supply curve, but implies nothing about demand.
That passengers suffer from a price surge does not assume an inelastic demand, or even a downward-sloping one. If you pay a higher price, you're suffering more, even if somehow it leads you to buy more of that thing.
Eh--"suffering" seems a bit dramatic; as economic transactions go, the up-front price quote by Lyft and Uber makes it pretty transparent and the options available to depart DCA put an upper bound on costs. But I was more referring to how Lyft and Uber make more money off of shorter, cheaper rides. They do make more from longer rides, because of percentages, but my understanding is that volume makes them much more money and that higher prices do depress volume.
By "suffering" I just meant "paying (someone, maybe another ride service) for it".
If higher prices depress volume, then some of the very drivers temporarily striking to raise the price end up paying for it, by ending up without a client. If all the drivers gain from it, then the airport demand for their Lyft services in particular (as opposed to demand for other ride companies) would in fact appear to be pretty inelastic. (Both seem plausible to me.)
(edited s/elastic/inelastic - I dun goofed. Thanks, Erik!)