Lucy is on the SSDI, http://ssdi.genealogy.rootsweb.com/cgi-bin/ssdi.cgihttp://ssdi.genealogy.rootsweb.com/cgi-bin/ssdi.cgi under her married name. She died 05 Jun 1990. Her entry has no LR or LB. If it is worth $27 to you, you can send for her SS-5, which will have her parents. If you know where she died, but not when, now that you have her death date you can try for a death certificate or an obit, either of which may have her parents.
The only John E Eyre they have was born in 1928, which makes it unlikely he was her husband. If you know she married a man much younger than her, he might be it. His SSN was issued in MO, and he died in 1993 in Centerville, Reynolds, MO.