I think it's a bit of a Marmite name, but I like Lyra better than Lydia.
For some people, the Philip Pullman connotations are too strong but it wouldn't worry me.
I also like the meaning. According to Google, the name comes from the Greek 'lyra', meaning 'lyre' (a small harp used by the ancient Greeks). Lyra is also the name of a small constellation which, according to Greek mythology, was shaped after the lyre of the legendary poet Orpheus. Its main star, Vega, is the fifth brightest in the sky.
It would be on my list for DD2 (along with your Audrey) if it didn't sound odd with our surname...