Where did you see the meaning "beauty"? It seems very unlikely to me. The Greek for "beauty" is
kallos, which clearly bears no relation to the name
Lydia.
Baby name books and websites often invent pretty or cute meanings for names that have 'boring' or unsavoury real meanings. This may be an example of the trend.
♦ Chrisell ♦
All we have to decide is what to do with the time that is given us. - J.R.R. Tolkien.