Thanks to @megleidy i got an answer to my question about the lemon tree from a real live law professor!

This is a great question.  First, accession law tells us that the fruits (no pun intended) of our property belong to us.  Hence the kittens your mom cat bears belong to you, as does the interest generated by your bank account.  So as a matter of ownership, the lemons and branch growth related to the neighbor’s tree belong to the neighbor.  Second, though, it is trespass to cause your property (such as branches or fruit) to enter someone else’s land without their consent.  This means that the neighbor is trespassing, and your friend has a remedy at law.

What would this remedy be?  In theory, your friend would be entitled to a civil injunction forcing your neighbor to prune his trees, and the neighbor would have to bear any costs associated with their incursion.  As a practical matter though these things are better addressed through self-help (i.e., friendly negotiation).  So while your friend may not be entitled to the trespassing lemons as a matter of law, taking them might be a half-joking way of saying “get these things off my land”.  Or perhaps better, maybe your friend _wants_ the lemons so can just take them if the neighbor is none the wiser.  Then we’d have competing torts: your friend would be liable for conversion of the lemons (because they’re not his, even if they end up growing on to his parcel of land); and the neighbor would be liable for trespass (via the encroaching lemons).