I wonder how you could enforce a life time ban?
Passenger lists are kept for a very short time only for reasons of privacy and space.
If you were a frequent flyer there may be some information saved about you but I do not think there is any reliable way of tracing ad hoc passengers.
Airlines, especially the smaller ones, may not have their own booking systems but rather buy space on a few very large booking engines.
I could foresee all sorts of problems with mistaken identities and about how much personal information is stored.
Jet2 is a relatively small airline and I cannot see anything that would stop this objectionable person taking her future business elsewhere.