E. Rossoni notes that this surname is fairly rare and would appear to originate in the area of the Strait of Messina, between Sicily and Calabria. According to Rossoni, it would derive from the patrician surname Luverà, documented at least from the 16th century, while the earliest traces of Luvarà go back to the pastoral visitation to Radicena of 1753, in which it is recorded that the altar of Saint Francis of Paola in the church of San Basilio Magno was under the ius patronatus of the magnificent Antonio Luvarà. As an alternative hypothesis, Rossoni suggests that the surname could derive from the Sicilian word lùvaru, the name of a kind of fish.

V. Blunda develops precisely this second hypothesis and presents it as the main etymology: the surname would be of Sicilian dialect origin and would come from the word lùvaru, meaning "sea bream", a marine fish of prized flesh and a habitual catch of the Mediterranean coastal fleet. Blunda suggests that the surname could have originated in the nickname of the fisherman who specialized in that species, or of the seller of the product in the urban markets of the coast.

G. Rohlfs proposes, by contrast, a Greco-Byzantine origin and links it to the family of Lugarà, derived from the Greek surname Logaràs. Rohlfs documents its presence in the city of Reggio Calabria, in the Nicòtera area within the province of Catanzaro, and at various points of the province of Reggio Calabria —Cittanova, the Bianco area and the Aspromonte—, besides noting its extension to areas of Campania and Sicily. He regards Luvarà as a sister form of Luverà and refers the reader to the entry corresponding to Lugarà.

The three sources therefore present divergent hypotheses: a patrician origin linked to Luverà with historical documentation in Calabria (Rossoni), a dialect etymology from the name of a fish of the Sicilian coast (Blunda), and a Greco-Byzantine etymon related to Logaràs (Rohlfs). None of the three succeeds in imposing itself as the exclusive explanation, and the surname admits the possibility of independent clusters of origin arisen in different regions without direct relation between them.