Lara was a Roman nymph, the daughter of the river Tiber. She bore Mercury the Lares, the household gods of the Romans. Ovid seems to have invented her name to mean 'chatterer' (from Greek laleo, 'to chatter', 'babble') for the tale in his Fasti ('Calendar') in which she kept on blurting out all she knew about the amorous designs of Jupiter and so had her tongue cut out and was despatched by Mercury to the Underworld.
The name does not seem to be connected with the city of Larisa (modern Larissa), in Thessaly, although oddly enough this could well be the origin of the modern girl's name Lara which acquired a certain vogue in English-speaking countries by way of the Russian name (and the popular 'Lara's Theme' in the film Doctor Zhivago). The modern name could also derive, again via Russian Larisa, of which it is a diminutive, from Greek laris, 'sea-gull'.