Jon, are you sure it's not "tresor?" I've found that many Italian songs are written in one dialect or another, and the forms of the words vary (e.g., "cchiu" for "piu" in the Neapolitan "O Sole Mio").

Sometimes the contracted words are written with an apostrophe, e.g., "tesor'" or "tresor'."

If "nana" is "lullaby" in Spanish, maybe "nanna" means "lullaby" in Italian. So, as you suggest, "Fa la nanna," could translate somewhat literally as "do a lullaby" and idiomatically as "go to sleep" or "sing [you] to sleep" or something like that. That seems to be what the context suggests.

I have a friend who grew up in Naples, so I'll email him and see what he says -- unless therer are gatti Italiani out there who can help.

Genie