Another possiblity, could be that one female tiger and one male lion was allowed on board to create Tions, or Ligers, ventually leading to new species of
feline we have to today
This would stop short pretty quickly as Liger (male lion, female tiger) and Tigon (male tiger, female lion) males are infertile, thus you'd only ever have the first Male Lion able to reproduce, once he died, there'd be no fertile males left. Cats gone.
Plus, getting a house cat from a Lion/Tiger crossbreed in 4500 years would require more evolution than even I can imagine ;)