Maybe. More likely someone will take her case for a percentage of any settlement. That said, 'justice' is not something you can depend on. It's more likely to get a settlement from spilling hot coffee on yourself than something like this - though this is a 1000 x more deserving.
Maybe her best bet is to fly United as a paying customer and then have a “slip and fall” incident at the ticket counter that will have every ambulance-chasing lawyer ringing her phone off the hook.