Not sure why you would use the router when you have a lathe. Just turn the end down to fit, with the unaltered end in your chuck. I've made many PVC and PEX boxes for laying tools and both materials cut fine on the lathe.
I'd probably use a 60d. cone tailstock in the end of the pipe or you could just turn something to fit over your live center. If you don't have a chuck, turn a mandrel to fit into your MT and jam the pipe over it at the headstock.
Not sure how long your tenon needs to be, but unless you are looking for a constant friction fit, I'd sure try this before using the router.
You also may want to experiment with using PVC in conjunction with PEX, as the ID of one may be close to the OD of another..............
Keep us posted, I'd like to see how you solve it.
rich |