A lean mixture will misfire, causing unburned fuel to enter the cat. Inside the cat all this extra fuel is ignited, causing the cat to overheat. The cat will eventually break apart internally clogging the exhaust system. Misfires are one of the catalytic converter's worst enemies. Lean mixtures which cause misfires will damage the cat.
Once a cat is clogged, an easy way to confirm diagnosis is to bring the engine up to operating temperature. Use an infrared no-contact thermometer gun to measure the temp on input and output sides of the cat. On a clogged cat the output temp will be considerably cooler. Example numbers for a clogged cat would be say, 400 degrees F input side, 150 degrees F output side.
On a good properly functioning cat the output side will be 50 to 100 degrees F warmer than the input side. Example numbers for a working cat might look like 420 degrees F input, 480 degrees F output.
A vacuum gauge and an infrared no-contact thermometer gun are two of the most useful tools to have when diagnosing a bad cat or restricted exhaust.