Travelling to Mexico with an Italian carta di soggiorno illimitata

According to this page (Mexican government Relaciones Exteriores website), if you have permanent residency in the Schengen Area you don't need a visa. Your passport needs to have more than 6 months of validity, and you'll need an FMM (typically you'd get these on the flight into Mexico, but can be done online and printed out).

No visa required If you are a citizen in the Schengen Area, UK, USA, Canada or Japan or if you have a permanent residence permit or a valid visa for any of those countries, you DO NOT REQUIRE A VISA to visit Mexico under the following conditions:

The purpose of your visit is tourism, studies or business. The duration of your stay does not exceed 180 days. You will not receive any remuneration at all from Mexico. However, it is necessary to have:

1. A valid passport with more than 6 months of validity (Mexican authorities require a passport to be valid for the duration of the stay in Mexico, but the transit countries and airline companies may have other requirements).

2. A properly completed Multiple Migratory Form (FMM). The FMM can be obtained from the airline or at the port of entry, but to expedite your registration at the border, you can now fill out and print it in advance in this link.

Remember to keep the FMM in a safe place during your trip! You will be asked for it at your departure from Mexico.

To gain entry with a Visa Exemption based on your residency status, the same page says:

Visa exemptions

Permanent residents must prove the permanent resident status to the immigration officer in Mexico at the port of entry

But as Hilmar points out in a comment, it wouldn't hurt to confirm for yourself specifically by entering your own details on the IATA Website Passport/Visa check page.