Two of my favorite resources for the Lawrence Co. area are the Marriage and Obituary database of the New Castle Public Library and the late 1800's books containing history of Lawrence County and its citizens. Ancestry has 2 of the histories, "20th Century history of ..." I think it is Lawrence County but it may be New Castle. The other book title starts "Book of biographies..." I don't know that they would help as far back as Lydia Rigby because they did a current resident and his ancestors. The biography I found was for a Seth Rigby.
The marriage/obituary database at the New Castle Library had 224 Rigbys starting in 1853 and 153 Magees starting in 1855. You can now order the articles by e-mail. The cost is quite reasonable. Early articles are not very informative, however, usually just a line or two.
I hope this may help if you haven't used these sources.