Short answer
Yes, a small piece of cooked, plain lamb is safe. Ensure it's lean, boneless, and has no seasoning or gravy. Because of your cat's condition, keep the portion tiny and occasional to avoid straining the kidneys. Offer it as a rare treat and watch for any digestive upset, contacting your own vet if you have concerns.
Lamb — Food safety facts
Safe to share · Cats · full breakdown on the linked food page
Lean, cooked and unseasoned lamb is safe in small pieces. No bones, no gravy.
The full verdict, portion guidance and serving notes are collected on the Lamb food facts page.