Well, first of all, if you want to refer to yourself as a Lupus or a Lyra, you have our permission. People develop affinities for various constellations, not just those included in the "zodiac." We recognize 13 zodiac constellations out of the 88 formally designated by the International Astronomical Union. Zodiac constellations are those through which the Sun appears to travel during the year. Of course, this motion is illusory, as Earth revolves around the Sun and therefore the Sun's position relative to the background stars changes continuously.
Presently, the Sun appears to be migrating through Virgo the Maiden. At the end of October, the Sun will move into Libra the Scales. The Sun then moves, in turn, through Scorpius the Scorpion, Ophiuchus the Serpent Charmer, Sagittarius the Archer, Capricornus the Seagoat, Aquarius the Water Bearer, Pisces the Fish, Aries the Ram, Taurus the Bull, Gemini the Twins, Leo the Lion and then back to Virgo the Maiden, and the cycle begins anew.
These thirteen constellations just happened to be aligned in such a way as to make the Sun appear to pass through them. If we wanted to (and were endowed with supernatural powers), we could alter Earth's orbit so that the Sun appears to move through other constellations. Neither Lupus nor Lyra can be zodiac constellations, however, because the Sun doesn't "move through them."
A person is considered to be a "Virgo" or a "Leo" if the Sun occupied that constellation when you were born. However, the astrological calendar hasn't taken precession into account. Earth's poles precess over a 26,000 year period and therefore the constellations aligned along the Sun''s path, called the ecliptic, shift stations slowly over time, by about one degree every 73 years. The dates the astrologers associate with the zodiac were valid about 2,000 years ago. For instance, the Sun was once in Aries on the first day of Spring. Now, it is in Pisces. For this reason, curiously, astronomers still refer to the first day of Spring (Vernal Equinox) as the "First Point of Aries."