You will need to advise LX that as your flight departed FCO, EU261 and subsequent ECJ precisions apply and that in your assessment, the reason for the flight delay from FCO would not be considered "extraordinary" according to ECJ readings of EU261.
Demand that the case be reopened, and compensation paid, based on this interpretation.
If they still don't budge, your only choice is to take up the case with the Italian enforcement body of EU261 - or have one of the claim agencies do it on your behalf.