Okay, another weirdness in indexing.
1860 Union Township, Lawrence, Ohio
Page after page is marked as Illegible, but the film is perfectly readable. As I recall, the first film posted was indeed too faint to read, but evidently it has been replaced. I found this first on Ancestry and then using that page as a guide found it in FS.
"United States Census, 1860," database with images, <i>FamilySearch</i> (https://familysearch.org/ark:/61903/3:1:33S7-9BSH-9XQP?cc=1473181&wc=7QGH-BY9%3A1589432777%2C1589422325%2C1589422372 : 24 March 2017), Ohio > Lawrence > Union Township > image 31 of 56; from "1860 U.S. Federal Census - Population," database, <i>Fold3.com</i> (http://www.fold3.com : n.d.); citing NARA microfilm publication M653 (Washington, D.C.: National Archives and Records Administration, n.d.).