Bit has to be harder than the steel being cut, lathe and tool post has to be rigid enough to hold it without any flex, and light cuts with lubricant/coolant are usually essential.
Only thing I've ever found myself unable to cut was some chromed shafting, and that is probably doable with the right tooling and lathe.
Overall, you are better off annealing hardened steel if it is at all possible and re hardening it after cutting. Annealing is pretty simple, heat treating to re harden it a bit more involved.