Lancia Thesis 2.0 TB - engine issue

[Flaviu]

Good morning everyone, how is everybody? So good to have found you!
I am a happy owner of a Lancia Thesis 2.0 turbo, 2002 edition, and sience my father bought this car, it has a small problem which I haven't been able to figure out myself yet:

The engine starting is OK, engine starts on cold/hot weather no problem what so ever, but even at 900 rpm the engine shakes and also the interior of the car.
The vibration is present 100%,it fades at higher rpm but still present, and also engine is having a weird sound; mechanics dont know what it is. Indeed, the engine mounts are a bit out of date but I bought a second Thesis, same engine, and the engine mounts are even worse, but the engine is working fine! No sounds / vibration.

Also, when driving the car : If i press the acceleration pedal smoothly and progressive, the engine is ok. But If i press the pedal without progressivenes, just asking the engine to deliver fast acceleration, I can feel the engine powering up, but after two sec the check yellow light comes up and I lose engine power.

I drive the car everyday, besides small electrical issues like rain sensor or parking sensor error, nothing related to the engine functionality recorded on tester.

Next days I inted to change the Lambda sensor, it has been measured and I know it's not working and wanted to ask you guys for opinions, If any of you had similar problem?!

Thanks