Axle Install

Did you take the center spacer out of the carrier case?
The best lube for O-rings is O-ring lube, a silicon product. It is sometimes difficult to find and is pricey. Second best is the treadmill grease, which is also silicon. And third is ignition grease, the stuff used on wires and point-cams.
The snapring is a stopper. When it hits the backing plate it stops, and then when you bolt on the retainer plate, it captures the snapring and thus the axle.
If you have not removed the center spacer, I have never heard of the second axle going in all the way.And if you try, you will fold your retainer plate over and ruin it.