Personally, I'm more particular and would not want to use a name that has already been used in my family unless I'm honoring the person with that name. For that matter I'm also avoiding E names and C names because there are already so many in my family.
That said, if it doesn't bother YOU and you absolutely love the name then go for it!
Lydia is a lovely name. I like the sound of it and it reminds me of the movie Beetlejuice.
Therese is okay, but I'm not crazy about it.