You want to use a compound slide. Most lathes come with one.
I am not trying to sound pompous with this. I am writing this with the belief that your lathe either does not have one or you are unaware it does and what its purpose is.
It is a small adjustable tool mount/slide that sits on the cross slide table that saddles the lathe bed. It can be set to the desired angle and has its own lead screw so that it can drive your cutter along that angle to the workpiece.
Here is a link to Sherline's. I know it isnt the best example of a full bore compound, in some ways but it was the first I found and it gives a picture and a downloadable instruction sheet on how to use a compound slide. It should give you a firm understanding of what I have so loosly described. Good luck and happy cutting.
http://www.sherline.com/1270pg.htm