Out of all the towns in the county, why Arnoldsville? The August 6, 1953, Oglethorpe Echo gives you an answer:
Consolidation of schools first began in this county in 1937 when a teacher resigned from the Liberty school in Flatwoods and the students were brought to Lexington for instruction. And then, according to Supt. Faust, in 1939, School Principal L.P. Green, of the Crawford school, invited pupils from Sandy Cross to come to Crawford, and after the idea caught on more and more pupils wanted to come to the school at Crawford from that section of the county. Then later, the schools in the Lexington school district began to send students to the Lexington schools, until by 1948 this movement has resulted in only one high school in the county, the present one at Arnoldsville, with only four elementary schools left, those at Crawford, Lexington, Maxeys and Glade. In 1937 there were 49 white schools and 63 colored schools in the county. There are 20 Negro schools in the county today.
Which makes Oglethorpe a bit strange. Most other school systems didn't give up their high schools until Minimum Foundation Program funds forced them (or if you were Richland in Stewart County, you fought the state 10+ years). The MFP made each county reevaluate its educational process for white and black students before it provided money.
So, in 1955, Lexington became the new home of Oglethorpe County High.
For football, it somewhat became the home of Oglethorpe County High. That said, Arnoldsville was in the same boat.
From 1952 through at least 1955, OC involved a third town: Crawford. Their field is noted as being Lakeshore Field. As this appears to be the only body of water near Crawford and as there is a Lakeshore Drive, I'm assuming it was located hereabouts.
And also, back in those days, Oglethorpe County was the Indians, wearing red and white. I don't know yet if the nickname change to Patriots is out of Native American sensitivity or out of an integration compromise.