Cut off parts, tap through using a long reduced-shank gun tap...in SOFT material. I don't think it's even possible in hard 15-5.
15-5 is basically 17-4 that costs more. "Soft" is about a 35C in the solution heated condition, what some call annealed, but its not "annealed", annealed is soft forever, until its solution treated, like the difference between in 6061 between A condition "0" and a condition "T0" they are not the same thing.
Yet when heat treated, you can end up anywhere between a 28 and a 46. I haven't messed with 15-5 too much, but in 17-4, even well into the 40's it machines better than it does in the mid 30's when its in the solution treated condition. It loses a lot of its "Stainless-y" machining properties once its heat treated and behaves much like a hardened alloy steel.
As for on a lathe, you aren't going to single point it. So you have to tap it. I wouldn't want to do it, especially blind.
Hopefully its a J thread so you can open up the minor, but your lathe need to be dead nuts square to try it.
At least its a fine thread, forces will be a lot lower than a course thread.
How many are we talking here. 500 or 20? I'd probably run them individually, maybe bar feed, add a back side chamfer into an undersized hole, and part. Then flip and tap as deep as I could with a standard tap, then finish by hand with the expensive long tap. But I wouldn't do that for 500 of them.