LTM means L
L39 is another way of referring to those types of lenses.
M39 is not really terminology for rangefinder lenses--like your Canon P--it properly refers to the few lenses that were made for SLR cameras that have the same thread as LTM lenses but are other wise not designed for nor correct for use on rangefinder cameras.
, some people do use M39 when they mean LTM.
As to collapsible lenses, that becomes a bit more complicated.
A collapsible LTM lens can certainly be used on just about any LTM body. There are a few combinations that you may not want to actually collapse the lens but there are several easy ways to mitigate this. I liked to wrap a fairly thick rubber band around the lens, just behind the front collar. That wouldn't impede the function and wouldn't damage the lens but it would prevent me from thoughtlessly trying to collapse it.
And, I can suggest reading this page for a pretty good over view of these lenses:
And come back with more questions!