The authors agree that the surname goes back to the olive tree as its main semantic base, although they differ on the etymological path proposed. F. Miranda holds that it derives from the aphaeresis —that is, the loss of the initial syllable— of the Spanish term olivera ("olive tree"), with a second hypothesis, regarded as less likely, which links it to the Latin liberius, derived from liber. Miranda further adds a possible toponymic provenance: the place called Livera, a hamlet of the comune of Pettinengo, in the province of Biella, in the region of Piedmont.

V. Blunda, by contrast, describes it as a Sicilian surname of dialect origin, derived from the word alivèra, meaning "olive grove" or "spot planted with olive trees". According to Blunda, the surname may have arisen as a microtoponym applied to the owner or worker of a particular olive grove, within an agrarian economy in which the cultivation of the olive had been central since antiquity.

As for its geographical distribution, Miranda notes that the surname is concentrated mainly in Sicily —with a presence in the Catania, Enna and Syracuse areas— and also appears in Puglia, Piedmont, Lombardy, Emilia-Romagna, Liguria and Campania.