I'm far from an expert on the subject and don't want to feign false hope of a miracle or anything like that, but what I can tell you from (albeit limited) personal experience is that the vets get this stuff wrong more than you'd think. My neighbor took her cat to the vet a couple years ago after it'd been attacked by her son's police dogs and they told her it had some sort of internal scarring and probably needed to be put down. Turned out after consulting with a specialist in the Boston area that it was treatable and the cat ended up being fine. Basically, she made it sound like they tried to extort her into getting an emergency procedure when it wasn't needed.
On the other end of spectrum, my parents adopted a cat that was about three years old (or so they thought). After about a year they took her for a routine check-up and were told she needed a tooth removed. They eventually obliged (and paid a fee of close to a grand) only to have the cat die from anesthesia-induced pneumonia two days after the operation.
So, although lymphoma is bit of a different animal with presumably a more straightforward diagnosis,
@king conn 's story does sound plausible to me. Much is still not known, even by those who know the most. My best advice is to trust your eyes - if the cat looks like groggy, demoralized, and defeated, then it's probably time (this was the case for my dog of 10+ years - she was so down and out that we made the choice to let her go even before we got confirmation from the test results that the cancer had spread). If the cat looks like it has fight left in it, then maybe it's worth pursuing additional treatment options provided they're affordable.
In the event that you do end up losing him in the near future, just keep trying to comfort and reassure your mom. Believe me, I'm the world's biggest softie when it comes to animals. I get that it can somehow actually feel worse in the short-term losing a pet than a person. But, much as I'd never care to admit it, they are replaceable - at least more so than people. I've done it. They're all quick to win you over no matter how bad you want to resist them and they're all easy to love no matter how many times they inadvertently kick you in the nuts.