What I'm curious about
matzemedia is how you secure the plexi in order to use it on the lathe. As solution6 has mentioned, it sounds like however you're doing it, it's putting quite some stress on the plexi. Using a lathe does seem like a real "sledgehammer to crack a nut" approach. Although the mere mention of a lathe does get me all envious.
Solution6 thanks for the description and illustration of the less extreme tool for the job. That's the same way I've successfully done the job too.
matzemedia if you don't have it already, get a tube of Polywatch to polish the sides of the plexi after it's been sanded. Diamond lapping paste (available in various grits) and toothpaste can also be used. But I'm sure you know all this anyway - I mean, you've got a lathe!