What does Lavanya mean?
From Sanskrit lavanya (लावण्य), 'loveliness, grace, charm, beauty' (literally 'saltiness', extended to attractiveness). Well established.
What does Bhavya mean?
From the Sanskrit भव्य (bhavya), 'grand, magnificent, splendid, noble, becoming'. A genuine classical adjective, used for both girls and (less often) boys.