It doesn't remind me of a saint's name.
It's very 1950s and the problem is that they run into each other so people will think her name is Leonette, as you wrote.
So why not Leonette? It's actually not bad and more interesting. I dislike hyphens and Leonette feels less dated.
Or
Leonie?
Lee is okay but everyone'd middle name pre-1970 or so together with
Marie,
Anne,
Ann,
Lynn and
Jean,
Joan,
Jane,
June.
Annette is sort of cute on its own but needs something more interesting to spice it up.
Please rate my list:
https://www.behindthename.com/pnl/6232