So what method is everybody using to get the wood from branch to lathe?
If it's big enough, I start ripping about 1/8" at a time from a side until I hit good heartwood, set it on the new flat and rip another side the same way, then set the fence somewhere around 7/8-1", cut slabs, then rip those down to square blanks. Anything too small to bother with that goes straight on between centers and becomes a round blank.
I have access to a pretty much unlimited supply of mesquite, all standing, some dead, so I have a lot of opportunities for pieces too narrow to make much other than pens. windfall pecan and standing dead oak are reasonably available on our land as well, but any time I can't find just the mesquite branch I want, the neighbors are happy to share theirs.