No, you do not have to trust the other person to not make purchases. You can simply set up the parental controls.

I understand why people are downvoting my original comment -- it is very easy to dislike Amazon, for many reasons -- but the fact remains that you can lend eBooks.

You just have to put them on a physical device first.

And you're allowed to put each eBook on up to 5 devices. That means you could, theoretically lend up to 5 copies at a time. Not just one.