I'd contact the paris Town Clerk, http://town.paris.ny.us/content/Departments/View/5
and ask about a copy of her birth record. The information on their web site is confusing.
You won't find her online until her marriage. Prior to 1850 only the head of household appeared on Census records.
I did find a copy of their actual marriage license but no parents were listed.
I'd look for the Cleveland newspaper after their marriage and look for their marriage announcement. Hopefully both sets of parents will be mentioned.
Lucy Taylor hall
Born: 11 Aug 1810
Died: 29 Oct 1886
Buried: Denison University Cemetery, Granville, Licking, OH
I'd contact the Licking County Ohio genealogical and historical society and ask if they have indexed newspaper death notices. Her parents might be in her death notice. Successful Searching!