Treadles are an archaic mechanical device. I grease the treadle plate pivots, the big wheel pivots and the ball bearings.
Mine moves so free I cannot set the machine with the needle up and have it stay there.
As for the machines. Metal moving parts get sewing machine oil. Metal gears get Tri-Flo grease. Plastic gears get nothing. Singer motors get Singer motor lube.
My machines run very smooth and the treadles can be run by one finger in the spoked wheel.
That's just what I've read and have found to work.
Joe