I'm so sorry about Lexie. I would definitely feed her whatever she will eat. The special diet won't help her if she's not eating it, and the girl's got to eat.
My cat Willa is in a similar situation, IBD potentially changed over to Lymphoma, bloodwork normal. My vet told me there's no point in a special diet. Let her eat whatever she wants.
The vet also suggested a trial of Chlorambucil, a chemodrug, just on the chance that it is Lymphoma.
Just like you I would not subject her to a procedure to prove that it is Lymphoma, so I think I will try the drug.
Your vet would probably be reluctant to prescribe it without a diagnosis, but it can't hurt to ask.
Willa's vet told me she would not do this with a regular client, since chemodrugs are not usually prescribed on a hunch and they can have lots of side effects. But I work there, so I won't sue her if Willa is not improving.
I hope that Lexie will bounce back!
Precious Lexie, please start eating.
Willa and I are sending best wishes to you and Lexie.

https://www.vetinfo.com/chlorambucil-for-cats.html