I've searched for Elda every way I can think of and can't find her in Utah or Idaho before her marriage either.
Do you have her, Henry or Emily's obituaries? Was her childhood mentioned in hers? Was she mentioned in Henry or Emily's?
I found a family tree on ancestry for Henry and Emily and family and asked the author to contact you. However, Elda wasn't included on that family tree.
I wonder if she was an orphan from another Lish family?
Oneida County doesn't seem to have a genealogy or historical society either.
Have you contact the Idaho State Historical Society, www.idahohistory.net/
? They do research and have a collection that covers the entire state. Successful Searching!