https://webb.nasa.gov/content/about/orbit.html
Some Technical Details: It is easy for an object (like a spacecraft) at one of these five points to stay in place relative to the other two bodies (e.g., the Sun and the Earth). In fact, L4 and L5 are stable in that objects there will orbit L4 and L5 with no assistance. Some small asteroids are known to be orbiting the Sun-Earth L4 and L5 points. However, L1, L2, and L3 are metastable so objects around these points slowly drift away into their own orbits around the Sun unless they maintain their positions, for example by using small periodic rocket thrust. This is why L1, L2, and L3 don't "collect" objects like L4 and L5 do.
Webb At L2
If Webb is orbiting the Sun further out than Earth, shouldn't it take more than a year to orbit the Sun? Normally yes, but the balance of the combined gravitational pull of the Sun and the Earth at the L2 point means that Webb will keep up with the Earth as it goes around the Sun. The gravitational forces of the Sun and the Earth can nearly hold a spacecraft at this point, so that it takes relatively little rocket thrust to keep the spacecraft in orbit around L2.
And Webb will orbit around L2, not sit stationary precisely at L2. Webb's orbit is represented in this screenshot from our deployment video (below), roughly to scale; it is actually similar in size to the Moon's orbit around the Earth! This orbit (which takes Webb about 6 months to complete once) keeps the telescope out of the shadows of both the Earth and Moon. Unlike Hubble, which goes in and out of Earth shadow every 90 minutes, Webb will have an unimpeded view that will allow science operations 24/7.
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In summing, L2 is actually only semi stable and still needs some rocket thrust to keep it in orbit around L2.
https://solarsystem.nasa.gov/resources/754/what-is-a-lagrange-point/
"L4 and L5 correspond to hilltops and L1, L2 and L3 correspond to saddles (i.e. points where the potential is curving up in one direction and down in the other). This suggests that satellites placed at the Lagrange points will have a tendency to wander off (try sitting a marble on top of a watermelon or on top of a real saddle and you get the idea). But when a satellite parked at L4 or L5 starts to roll off the hill it picks up speed. At this point the Coriolis force comes into play - the same force that causes hurricanes to spin up on the earth - and sends the satellite into a stable orbit around the Lagrange point".