"Let's eat apples!"
Translation:Lass uns Äpfel essen.
You’re right, I was only thinking about the “leave place x” sense and forgot about“leave x in state y”. Apologies.
I thought one would use "lassen" as "leave" only if it meant something like "let it (continue to) be (in some way)" as in "lass die Tür auf". But wit "ich habe das Buch zu Hause gelassen" this isn't the case, so what is the actual difference between "verlassen" and "lassen"? Could one say "ich habe das Buch zu Hause verlassen"?
No, you can't.
You can das Haus verlassen ("leave the house" in the sense of "quit/abandon/vacate the house") but you can't das Buch verlassen.
That would sound to me as if you were in a romantic relationship with the book and then you dumped it -- because you can also jemanden verlassen (to leave someone, i.e. to abandon the relationship). Or as if you lived inside the book and then you came out of it and went somewhere else.
So lassen is something like "leave something in a state or position" (you're "on the outside" of the thing), while verlassen is something like "go out of" (you used to be "on the inside" of the thing) -- sometimes more final, "abandon", sometimes more temporary, as when you leave the house in the morning.
There's also zurücklassen and hinterlassen, both "to leave behind" but not quite identical.