For example, when I first ran LP I ended at around 285 on the squat. After LP I ran some bodybuilding type program. Then, I came back to LP a few months later and ran it again, and this time ended at a 345 Squat.
That may be one component of how/why you got further, sure.
Additionally, the effects of your “bodybuilding program” probably played a role – i.e., you probably had more muscle mass and a higher baseline of strength on your second run through. There may have been some significant differences in your mental approach to training, too.
I think the mental aspect had a lot to do with it for sure. The muscle mass aspect is almost certainly true as well but not because of the bodybuilding program: I dieted down from 185 (end of LP1) to 165 (starting weight of LP2), but my starting bodywweight for LP2 was still higher than the start of my LP1 (155).
I guess one reason I’m wondering is, let’s say that someone comes to you who is already reasonably strong (let’s say a 405 1RM, or 375@8, somewhere in there; demographic: 25yo male, 200bw, 5’10”) but who has only been doing bodybuilding type programs for months and months and months, with the occasional set of fahve thrown in there (after a burnout of course, however) along with an occasional max out (your typical bro workout). It would still be appropriate to start that person off on some sort of brief, and perhaps close cousin of, an LP right? Simply because he is, at this stage in his training, sensitive to sets of five across, as well as higher frequency (as opposed to body part split).