Coach very frequenttly the hottest load is not the most accurate. That seems to hold true with both rifle and pistol.

3.6gr is the max load according to the Hodgdon manual for LRN- I'm sure you realize that. But what you may not realize is that coated bullets frequently behave more like JMJ or even JHP in terms of the amount of powder you can safely load. It becomes a (literally) case by case basis. In other words, your spent brass is the best indicator as to whether you can load them hotter or not.

With that all said . . . seriously, if it were me, and I know this is going to shock some people; I wouldn't load them hotter than they need to be to meet your intended use goal.

If it is "bullseye" - stay light if the pistol cycled reliably. Only go hotter if there is a need to.
If it is "self defense trainers" - go as heavy as you can safely, that is most likely to best represent factory self defense loads.
If it is "defensive ammo" - load that shit just as heavy as your gun(s) will tolerate.

It will not surprise me if some other folks have some opinions different than mine. All I can really do is offer my perspective. And Lord know I like my ammo like my women; HOT.