[Symmetry]

I just wanted to add that L2 (and L1 and L3) are unstable in that if a satellite is a bit further than the exact point it will tend to get ever further with time and a satellite that's closer will tend to get even closer. But the closer you are to the exact L2 point the smaller these tendencies are and the amount of fuel needed to remain on station is minimal, a satellite will just eventually run out some day and fall out.

The L4 and L5 Lagrange points are the stable ones. Something that finds its way there is going to stick around indefinitely. That's why many planets have asteroids in the L4 and L5 they make with the Sun. These are called Trojan asteroids and the names of the Jupiter-Sun Trojans are taken from the Trojan war.

[hanoz]

So how can this craft orbit a point that is not a gravity well but a gravity hill, so to speak?

[Symmetry]

It's a gravity saddle! From Earth's perspective it's a hill in the r direction but a well in the phi/theta directions. To orbit at a location always visible from Earth it needs to move in the phi/theta directions but moving the the r direction doesn't help, so it doesn't.

[Latteland]

And you clearly know this but i had to refresh my own knowledge of spherical coordinates - https://en.wikipedia.org/wiki/Spherical_coordinate_system