The Natural Balance Venison & Green Pea (canned) is what I feed. I'm fairly happy with it and the girls love it! It's true that these ingredients are often touted as being suitable for cats with sensitive systems. It has not been recalled.
As for lamb and rice, Lick Your Chops makes one but I don't like their list of ingredients and wouldn't recommend it. Iams and Science Diet are crap - avoid like the plague.
The reason lamb is often recommended is because it's meat that cats wouldn't typically eat. It's not the lamb itself that's important.
If your cat does have what I would call a sensitive system, you can try other meats, such as the venison. If you go to a quality pet store, usually independently owned, they may have a wider selection of good quality foods that you can try.
It's sometimes not the meat but the other ingredients that disagree with cats. Items like soy, corn and wheat are common allergens.
If you buy a good quality food, they won't have those items.