A mixer setup will never keep a more sophisticated petrol ECU happy by directly using the Lambda sensor outputs to control LPG mixture. I'm guessing the LPG fuelling has been out for some time and this has perhaps killed the Lambda sensor and cat.
In addition, it results in silly values in the block learn tables of the ECU meaning running on petrol is then affected.
I would run it exclusively on petrol until after it has passed the test.
With the Lambda value at the exhaust gas now somewhere near correct another italian tune-up might wake the cat up (I would say a fast motorway / main road cruise is the most effective way to wake a cat up). Failing that a second hand one from a breaker is probably the best route as aftermarket ones tend to be poor quality.
Beware the new cat might go the same way if the main problem is not addressed, but it does require further diagnosis to be sure what's going on. Get it through the test on petrol and then, once it's back on the road, we need to take a look at the live data and see what's going on.
Kevin