It is the semantics of metallurgical and industrial definitions that interferes here; the steel doesn't care one way or the other. Many metallurgists and industry guys have a differing definition of "normalizing" than we do. Although I have yet to find a text that indicates that one must soften or stress relieve the steel in order to normalize it, many feel that is the case. Since I look at normalizing as a process of refining, redistributing, and evening or homogenizing internal structures and stress/strain, there is no problem with my normalizing O1, L6 or any other deep hardening steels, although I prefer not to do anything with a true air hardener, just not my cup of tea.
One just needs to remember that the rules change a bit when normalizing deep hardening steel. You will get no results if you treat it like a shallow hardener (well a little bit in the heating, but no marked grain refinement). In order to refine grain one must cycle it through a transformation from austenite to another phase/structure. So if you simply cool it until it loses incandescence, like say 1084, there will be no significant change since the pearlite transformation is suppressed. Instead one will have to rely upon upper bainite to do the job for you and this will require that you go to around 700-750F instead before reheating. I have heard absurd claims from folks that L6 cannot get as fine a grain as other steels they tried, this is because they didn't understand this simple principle (one more reasons I am not a fan of assumptions made without metallurgical research to support them

). Use the magnet when normalizing, as soon as the stuff regains magnetism you can reheat it and achieve grain refinement. Start out with higher temperatures to move the carbides around and then go a little cooler. Never go from 1700F or better to room temp or cracking could occur in 01 or L6; instead bring it down in steps so that the final heat is from a uniformly fine structure.