The condition of the cat has got nothing to do with the Lambda system. There is no sensor downstream of the cat, so the system cannot tell whether the cat is working or not. In my experience cats never wear out - not in 390,000 miles anyway. I would suspect a poor electrical connection somewhere. Is the engine properly earthed - there is supposed to be a separate small braided earth lead to the top of the engine. For some reason the main starter earth is not sufficient.