You did not tell us what lathe you have or post pictures of the left end of the spindle installation, so it is difficult to visualize what you have or what you are doing.
I have a Chinese 13x40 lathe and am building a hand wheel drawbar arrangement for it, and it will include a spider. The left end of the spindle, starting from the far left end, first has a smooth inner and outer bore for an inch or so, then has a few external threads extending beyond the spindle end play adjusting nuts. I have seen people make an internal thread on their spider to fit those spindle threads, and perhaps that is what you have in mind. I can see no good reason for doing that, it is difficult, it only engages a few threads at most, and I see no reason why it it needed, and good reasons why you do not want it that way. I made my spider/collet closer adapter so it has a counterbore to clear the threads completely, and just rests against the spindle nuts. I then added some threaded brass plugs I had laying around to hold the adapter to the O.D. of the left end of the spindle by friction only, screwed through the adapter like the spider bolts, and pressing against the left spindle end O.D. If you crash something while working with the collet closer, it will stop the collet, but not the spindle. If the adapter is threaded on to those few threads, it will possibly tear the threads off the left spindle end before all the damage is done. With my design, the adapter is held only by friction of the brass plugs against the spindle O.D., and is able to slip on the spindle any time things do not want to turn at the same speed, for whatever reason. The collet closer tube normally holds everything together during use, so the brass plugs just keeps the spider/adapter from falling off the spindle when the collet closer is removed.
It sounds like you are just wanting a spider, so my thought is that the spider should be free to rotate on the spindle if necessary. There is no good reason to have the spider hard keyed to the spindle. Think about what happens if the work stops turning but the spindle does not.