to leave to , to give (In the sense of "pass into someone's possession". Sounds formal.)
to leave up to ("jemandem+Dat etwas überlassen" leaving a decision or choice to someone.)
In this article, we'll talk about the quirks of using "lassen" in past tense and we'll explore its prefix versions - with a special focus on "verlassen".
lassen, überlassen, ablassen, einlassen, erlassen, verlassen,
The core idea of this root was:
letting go, slacken off, relenting
And we can still see this sense in the English offspring, like last, let, lenient, latter or late.
By the way, the words relax and and release, though they would fit in here, apparently come from a different root.