I don't know about Welsh -- did your greatgrandmother know French, though? There is a novel written by the French author
Nicolas des Escuteaux in 1605 titled
Les amours de Lydiam et Floriande.
http://en.wikipedia.org/wiki/Nicolas_des_Escuteaux
Lydiam may also simply be a name that arose when someone did not know how to understand Latin records, because the name
Lydia becomes Lydiam when it is "declined" in Latin in certain parts of speech, as in marriage records written in Latin:
http://www.genuki.org.uk/big/LatinNotes.html