IANAL and I am from US so I am not familiar with animal laws in your country but this may help start get some gears rolling on what you could do. is cat micro chipped or ever been taken to the vet so L can prove ownership? Do you have pictures or proof of the cat being neglected? Would the roommate agree as a witness to saying the cat is neglected? You may be able to make a case of animal neglect and report it to your city's animal control. I mean if she's going out of her way to gather witnesses to prove the cat being hers and never giving consent to giving it away then you should be willing to gather your own witnesses to prove of her neglect. They will fine L for not vaccinating her cat at least and in order to dismiss case they must take it to a vet and do all city's requirements of vaccinations and city registering, etc.

If cat is not registered or microchipped with the city then technically it is not R's property and they can't really claim the cat as theirs but it really is a grey area depending on the police who is handling the situation if they become involved. You could register the cat with the city, getting it micro chipped and vaccinated if you really don't want to give the cat back but I understand R doesn't want this to escalate since R and L are sibilings.

I would also look into animal abandonment laws for your state or county. If you can prove that L knew it was in your possession but didn't bother contacting you about it for some time it may be considered abandonment.

But you may have no choice but to give it back or give it up to animal control to handle the situation. Try talking to L and see if you can buy the cat from them or they give it up.