My method for setting lathe tool offsets in LinuxCNC uses an electronic edge finder designed for the mill. This has an accurate 0.2″ cylinder on the end and when mounted in the chuck provides an excellent reference for setting tool height and the X and Y offsets for tools mounted in the quick change tool post.
Don’t do as I did and rotate the chuck when you are doing this or you will scratch up the edge finder.
I use a trigon insert tool as my reference – tool offset zero in X and Z – as it can turn and face. This is used to set the G54 work offset. The other tools are set using the touch-off buttons to set their offsets relative to the reference tool and thus to the G54 work coordinates.