"Let's eat apples!"
Translation:Lass uns Äpfel essen.
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.
Technically not, though it’s very unusual. I can’t think of a lot of situations where I would prefer that form over the one with lassen. Sometimes with very short sentences (just verb + wir) you do hear it, e.g. gehen wir or fangen wir an. But even there I’d say the form with lassen is at least equally common.
Why "lass uns" and not "lassen uns"?
Formally, this is a command addressed to one or more listeners, so you use the usual imperative (command) form:
- Paul, let's ... = Paul, lass uns ...
- Julia and Maria, let's ... = Julia und Maria, lasst uns ...
- Mr White (and Mrs Brown), let's = Herr White (und Frau Brown), lassen Sie uns ...