I have had to cut a lot of non-standard threads lately and the lathe is the only way to accomplish that. For about the last forty years I have always sharpened the tool bits by eye on a bench grinder using a fishtail gauge as the template to compare the tool bit tip with, and that's okay for occasional jobs and somebody with good eyesight.
About four years ago I bought thread cutting tool bars for doing both external and internal threads, but the carbide or ceramic inserts cost $15 each and snap off way, way, too easily when the tool bit comes to the end of the cut, that is an especially bad problem down in a hole when doing internal threads, even with the carriage travel stop set to stop the carriage before the tool point bottoms out. The tool holders I have can't be turned upside down so the lathe can be run backwards, which is the way to avoid the end-of-cut problems. I still use the tool bars when the end of the thread cut runs out into open space, but when the cut stops up against a shoulder, forget it! That is $15 guaranteed to be gone from a broken threading insert no matter how carefully the tool bit is used, they MUST run out into open space to prevent end-of-cut breakage.
I use a parting tool for thread cutting, its narrow width and vertical stability are ideal for threading and because they are narrow they are darned easy to sharpen to a 60° point. Getting that point to exactly 60° (or 55° for Whitworth threads used on Enfield, Mauser, and Mosin-Nagant rifles) every time can be a problem when the tool bit needs to be sharpened several times per job, so I made a guide for my bench grinder that works great and is extremely simple. Making the angle on the guide is the toughest part since the included angle of both right and left guide straight edges have to be at exactly 120° (110° for Whitworth) angles.
My bench grinder tool guide is made from a piece of 1/4" x 2" x 3" hot rolled flat stock with a 1/4" slot cut in it so it can adjusted in and out from the grinding wheel and is bolted to the grinder steady rest bar with a 1/4-28 grade 8 bolt. I cut the guide at the 120° included angle in my millimg machine by re-mounting my vise on the mill table at a 60° angle. I cut one side of the guide and simply turned it over in the vise to cut the other side. It works great and now I can accurrately re-sharpen a threading tool bit in seconds. When the guide is in the way of using the grinder it is easy to get off. I also drilled a hole off to one side of the threading tool guide plate so the guide can be put back on the steady rest at the 59° angle for hand sharpening drill bits.