Libra is one of the twelve signs used in astrology, and it keeps its capital L. As the name of a sign it is uncountable: her sign is Libra, she is Libra. The picture behind the name is a balance, a pair of scales, and horoscope writing often ties that picture to fairness and to weighing both sides. The dates move a day either way depending on the year, and a different system of astrology uses a different stretch of dates altogether, so treat the ones you see as the usual ones rather than as fixed.

English lets the name of a sign stand for a person born under it. This one is countable, so it takes a and an s: I am a Libra, the two Libras in our class. That is the clearest way to tell the two uses apart: an article in front means a person. People often follow it with a claim about character — Libras are said to be fair — and the phrase are said to keeps it as an astrology belief rather than a fact.