I looked in History of Ross and Highland County and reference to Lemons in Highland County, Ohio. page 368-In Hillsbourgh, a business "Hanlon and Lemon", Marble and stone works. They employ 4 people. page 381-The Masonic Fraternity in Hillsbourgh,lists as an officer,John C.Lemon, J.D. page 387- The Captain of the Fire Department at $30.00 per year is S. Lemon. page 454- Thomas Peale has as his third wife, Eliza J. Lemon. Her father, Samuel Lemon moved to New Market before the county seat was removed (1808) to Hillsbourgh. page 472-In Berryville, Washington Twp, listed as a store owner, Joseph Lemons. pagw 485-In New Market, in the fall of 1802, George Caley and Isaac Lemon settled. page 488- Samuel Lemons came at the same time (1814) and settled 2 1/2 miles north of town (New Market). He raised a large family and his decendants have been numerous in the township for many years, page 488- Isaac Lemons and John Lemon came and largely increased the the settlement. Their families were large.
I believe you need to search Highland County Records for most of the Lemon family. The above named book also lists several different spellings of Lemon name when the men were in service in the Civil War.