Language Of Confusion: To Leave

I can’t believe I haven’t done the word leave before. I’ve done left, as part of left and right, but not leave. I’m just surprised it never occurred to me to etymologize leave.
 
Leave comes from the Old English laefan, which is also just to leave. That’s from the Proto Germanic laibjanan, from liban, remain, which can be traced all the way back to the Proto Indo European leip-, which means… to stick or adhere. Yeah. I mean, it going from stick to remain in Germanic I can see, but I have no idea how it got from there to what we use it for. Of course, that’s not as weird as the other version of leave—as in taking your leave of something—not being related at all. That one comes from the Old English leafe, leave, permission, or license. It’s from the Proto Germanic laubo, from the Proto Indo European leubh-, to care, desire, or love. That makes even less sense!
 
Now let’s look at leaf, like what comes off of trees. It comes from the Old English leaf, which means the leaf of a plant or the page of a book. It’s from the Proto Germanic lauba-, which as far as I can tell, is not related to laubo. It’s thought that comes from the Proto Indo European leab(h)-, which again, doesn’t seem to be related to the similarly spelled word above. Its definition is actually to peel or break off, which does kind of seem like something leaves would do. This also means that the leaves that fall of trees have nothing to do with either of the other usage of leaves.
 
And there’s more. Leaven is the word for what you add to dough to get fermentation. It showed up in the mid fourteenth century (an actual date!) from the Old French levain, from the classical Latin levamen, which actually meant alleviation. It’s just that for some reason, Vulgar Latin took that word as meaning something that lifts or raises in a more literal sense, and that’s why it was associated with bread. It’s from the verb levare, to lift, from the Proto Indo European word legwh-, light (as in, not heavy).
 
TL;DR: Nothing with leave in it is related to anything else with leave in it.
 
Sources
Online Etymology Dictionary
Google Translate
Omniglot
University of Texas at Austin Linguistic Research Center
University of Texas at San Antonio’s page on Proto Indo European language
Tony Jebson’s page on the Origins of Old English
Old English-English Dictionary
Encyclopaedia Britannica