Births were first recorded in Lucas County in 1867 so that eliminates any possible birth record unless you know if she would have been baptized and in which church.
There seems to be some confusion as to when Louisa was born. In the 1900 census she was in Saginaw, MI, married to Robert and she was born August 1856. But on her death cert, her daughter said she was born 24 Aug 1861.
Also, her death cert says she was married to Robert but in the 1910 and 1920 censuses she was a widow. Perhaps she remarried a Robert Palmer.
Louisa's father's name looks like MARDAND or MARDANS.