Yep you are right. Protein in the urine is due to kidney damage and found in animals with renal insufficiency/failure. It is usually in the later stages of renal failure that protein can be detected in the urine so your grandmothers kitty would almost certainly have chronic renal failure, poor baby. A low protein diet is best if the kitty will eat it but it is important that if she wont eat this diet that she eats something. Cats with CRF often lose their appetite and so a low protein diet is not always practical but its definitely worth a try and will help prolong the disease. But your vet should have discussed other options also if it is CRF. It could also be acute kidney damage from some kind of trauma or infection.
The other possiblity is a bad case of cystitis which can cause damage to the kidneys in which case the cat needs antibiotics and a special diet like Hills cd-s at least temporarily till the infection clears. But I am guessing since the vet recommended a low protein diet that it is kidney failure. Make sure kitty has lots of fresh water available always too!