Thanks for the links, brino. It appears that using a chain to connect the treadle to the shaft was fairly common. I couldn't tell from the original photo if the driveshaft was bent or not, thought it might have a ratcheting sprocket to drive the flywheel, but apparently not...
I built a treadle lathe about 20 yrs ago, and demoed it at various harvest shows. No one seems to understand how a treadle works, they would just mash down on the treadle without any regard to where the flywheel was positioned. A ratcheting sprocket would solve that problem.