The trouble is, using the router and that small of an end mill, you have a good chance of breaking quite a few bits. The router probably has a good deal of run-out. You also need to make sure your lathe is clean and the carriage is moving as smooth as possible. Any runout or sudden vibrations can easily break your bit.
Like the other poster said, make a cut and measure it. It might be hard to measure that thin of a slot. Maybe try drilling a hole with a .125" cutter and measure that. Any movement in the cross slide though will compound your results.
There's not really an easy way to figure it out except by knowing your machine and trial and error.
When I first started doing my barbell type rings, I did them on the Hightower Machine. I first tried a dremel, but they are pretty bad. I bought a Proxxon tool, which is a lot like a dremel, but it a lot more accurate. Some of the rings I did on manually like that came out better than some I did on my first CNC machine.