I've got no lathing tips for you because I've only used a lathe once and I'm more of a carver but you've done a great job there for a first attempt! For the finish I'd recommend smoothing it out with some 240 grit sandpaper, cleaning it off with white spirits or similar then giving it a couple of coats of Danish or boiled linseed oil. The grain will look absolutely beautiful.
Be sure to post an update photo!