In 1799, outside the small settlement known as Middletown (now Coraopolis), there were 39 documented households in what then comprised Moon Township in Allegheny County, Pennsylvania. One of these was the household of a John Marshal on land that was part of the John Ward grant. Another was the household of a John Marshall on land that was the Henry Bryan grant.  Both of these men appear in the 1791 tax rolls for Allegheny County, PA, and I think it very likely that one of them was the father of a Lazarus Marshall, born c. 1786.
By 1824, Lazarus Marshall was residing in Meigs, Muskingum, Ohio, as is evidenced an except from History of Muskingum County regarding the formation of a Methodist Episcopal worship group :
In the year A.D. 1824, Rev. Mordecai Bishop preached in the southeast corner of the township, and formed a class at Lazarus Marshall’s.
The members of that class were : Lazarus Marshall and his wife, Mary, David Blackburn and wife, Arthur Ginn and his wife, Mary, James Mitchell and his wife, Mary, James Guy and his wife, Deborah, William and Mary Guy, and Elizabeth Blackburn.
Another source duplicates this information and specifies that Lazarus Marshall’s residence was in the southeast corner of the township. 
Looking at the 1820 Census records for Meigs Township, I find nothing that might fit this Lazarus Marshall.
Although I’ve found nothing to connect the ancestry of Lazarus Marshall with that of the Richard Marshall (c. 1757) also living in Muskingum County, they seem to have appeared in Meigs Township around the same time. Marshal Stults, the grandson of Richard Marshall, married Sarah Peirce in 1832. She was the daughter of a Lewellen Peirce who was one of the initial dwellers of Meigs when the township was formed in 1819. The marriage was officiated by John Hammond, who was elected Justice of the Peace (along with Lewellen Peirce) in 1819 and is also listed as a Justice of the Peace (along with Lewellen Peirce) in 1832.  Also of interest is that Marshal Stults became a carpenter by trade.
Census records show an Edmund Marshall sometimes living near Lazarus Marshall. A biographical sketch indicates that this Edmund, born in 1817 in Pennsylvania, was the son of Lazarus Marshall, also born in Pennsylvania. This biography also reports that Lazarus was a carpenter who had a family of six children. 
There is a record for the grave of Lazarus Marshall at Find A Grave, which gives June 22, 1854 as the date of his death and lists him as buried in Oakland Methodist Church Cemetery. This was the first cemetery in Meigs Township, associated with Hopewell Church 1830-1846, which became a Presbyterian Church 1846-1878, and then several iterations of a Methodist church. In addition to Mary Marshall (wife; b. unknown; d. September 8, 1845), we find in the same cemetery a joint headstone for Albert Marshall (b. August 24, 1842; d. November 27, 1911) and Sarah I Marshall (b. 1844; d. 1913). This suggests that this Albert, son of George Marshall, is a grandson of Lazarus and Mary.
 Jockers, Robert A. (2006) Forgotten Past: A History of Moon Township, Pennsylvania. Xlibris Corporation.
 Everhart, J. F. (1882). 1794. History of Muskingum County, Ohio: with illustrations and biographical sketches of prominent men and pioneers. Columbus, Ohio: F.J. Everhart & Co.
 Biographical and historical memoirs of Muskingum County, Ohio: Embracing an authentic and comprehensive account of the chief events in the history of the county and a record of the lives of many of the most worthy families and individuals. (1892) Chicago: Goodspeed Pub. Co. Available from Google Books https://books.google.com/books?id=ASBEAQAAMAAJ.
 Everhart, ibid.
 Commemorative biographical record of the upper Wisconsin counties of Waupaca, Portage, Wood, Marathon, Lincoln, Oneida, Vilas, Langlade, and Shawano. (1895). Chicago: J.H. Beers & Co. Available from Google Books https://books.google.com/books?id=VElEAQAAMAAJ