Upvote:3
The Irish Government has a website that tells you if you need a visa. It only asks about your nationality, not about permanent residence. From this, it appears that only your nationality matters and, as a Lebanese national, you need a visa.
If you don't want to trust this argument of "They'd ask about your permanent residence if it made a difference", you can look for more information on the website of the Irish embassy in Italy or telephone them at +39Β 06Β 585Β 2381.