No if doesn’t, there has been an actual study/evaluation done by Larrin (Knife Steel Nerds) that is as “scientific” as anything out there...the gist of it was that:
A) H1 does not work harden
B) the edge is not any harder than the spine
C) there’s nothing special about H1 except that it’s hard enough to make a decent knife steel while being extremely corrosion resistant. Most steels that are that low on carbon and/or that corrosion resistant can’t get hard enough to make a good blade steel. H1 makes a decent one, albeit not that good.
Unfortunately, there is a lot of misinformation out there, sadly Janich (who works for Spyderco) keeps repeating a story about work hardening H1 and there’s really no way it can be true.
As for LC, it is hardened more conventionally and the nitrogen level is amped up by the PESR process to a level that is high enough for a small amount of chromium nitrides to form, this helps wear resistance (a small amount). There are other nitrogen steels that have much higher levels of nitrides, be it vanadium or chromium.