The left handed screw is usually on the crown wheel and breaks off in the brass plate. These can usually either be worked back out or dissolved out with a alum solution. One thing to note though is Not All left handed screws have the 3 slots or any other markings to identify them! You’re right..it’s not fair!
I’m not sure what movement is used as the LP 38 but the LP 37 is a Font (FHF) and I believe it does use a left handed screw on a large crown wheel. I’m not positive about that though. Lucian also used ETA etc. movements. I’ll try to find a link to a LP 37 pic if there is one and will post it up here so you can check to see if it’s a similar movement. Also if you have a Bestfit catalog you can identify it through setting mech pics.
I’ll be back with more info if I can find some for you.
Also…don’t sweat it. We’ve ALL BEEN THERE!
Take care for now,