2004 Lincoln LS engine code

P0408 isnt a cat code, its an EGR code...P0430 is the code that fits your question? What code do you actually have?

If it is P0430 Then it could have been caused by the misfiring, check the cat for damage to the inside, or honeycomb bed. Rap on it and see if it rattles, if it does the bed has broken up. Heres two pictures of the cat and O2 sensors before and after low effeciency is when the rear sensor switches fast, like the front one, an efficent system switches slow and is almost flat on the rear sensor.

If you have P0408 let me know, there are a few Tech bullitens on this...

Well cars dont heal themselves, but I would check the response on the sensor two, downstream of the cat (behind), it may be a sensor out of range. Other than that, it means the cat is dead anyway, so it means you wont pass your next inspection, if the cat isnt clogged, it wont hurt to drive it, but I couldnt say without looking at it. If you have any lean codes, fix it now, lean running engines can be damaged!