Oh ok, I don’t believe there is an orbit per say, once it gets to the L2 point it stays there. Far enough out 93,000 miles from earth to orbit around the sun.
It actually orbits the L2 point.
I have seen two illustrations - relative to Earth, one polar orbit, and one equatorial orbit.
The polar orbit makes the most sense - always facing away from the sun.
An equatorial orbit would require constant fuel use to keep the sun behind it.