I am by no means the man to talk to when it comes to troubleshooting car issues, however, the implications in your post seem to narrow it down to one of two things: the lambda sensor and the decat. If you disconnect the sensor you are effectively by-passing the systems ability to monitor exhaust gases, hence the reason the car runs ok without it. Therefore, it would then seem that there is an fuel mixture problem, so what could be causing that? Well, you decatted the thing didn't you, and that changes the exhaust gases and the problem started after you decatted. It seems to me that must be the decat! Or is that too simple. Put your cat back on, reconnect the lambda sensor and if it goes ok, you know 100% that its the decat.