Engine loud vibrations at ignition only

I have a Skoda Fabia 1.2 Hatchback from 2007 (6Y,BME) which only yesterday started to have a strange symptom soon after ignition. As soon as I turn the ignition, you can feel the motor vibrate louder than usual, whilst struggling to reach the nominal 1000rpm, almost going into stall. Then after a few seconds of quick jumpy vibrations, the car finally settles on the 1000rpm mark. I can drive it then as usual, no loss of power or whatsoever. The only thing I would say, and I am guilty of leaving it for too long, is that I had, a couple of months back, an ECU warning light shown on the dashboard. When I went to the mechanic, the fault came as "P0420 Bank 1. Efficiency below threshold. Output does not have a contact to positive". I basically ignored the problem and now this happens, could it be related? I went to the mechanic to see if we could take the lambda sensor off, but the mechanic struggled and told me that it's possible the oxygen sensor may have melted and therefore soldered itself to the cat converter, but , is it possible. My main question would be whether somebody knows why suddenly my car has started experiencing such symptom, the rest it's information that could be relevant, or not. Thanks very much.