Lyra is a constellation name taken from the lyre of Orpheus. It contains the star Vega and thus could make a melodic choice for a parent interested in music, astronomy, or mythology. It has more depth and history than Lyric, is more unusual than Lila.
Lyra was chosen for their daughter by Sophie Dahl and Jamie Cullum. Lyra Belacqua is the heroine of Philip Pullman's His Dark Materials series,, seen in the movie The Golden Compass.