I don't know if this right but I'll throw it out there for discussion.
I'm going to say the L points seem like gravity Eddy currents ( sort of my minds picture in layman's terms). Created by earth and moon interaction with each other and both tied on by the sun. I'm sure the math isn't right but it's my dumb it down thoughts.
your layman's question is quite profound. I am a math nerd .. but this math is way beyond me however.
lot going on in that diagram .. much more tortured math and physis presented in
TWO dimensions, with some infinities mixed in.
The lines are depictions of gravitational equipotential. yes, all those massive objects, sitting "in" gravity wells (the "deepest" well under the yellow "sun" object, much more massive that the blue dot),
oh, the moon is NOT drawn there either - it must have some effect on the math but perhaps not as much as I am thinking, are interacting with one another.
the other "gravity well" caused by the Earth (imagine a bowling ball on a stretchy fabric .. that's shape in that setup is analogous to a massive celestial object deforming "spacetime"), causing things to "fall toward the well (but not go in IF they have sufficient momentum to go into orbit (is the earth
Here's a thing as pedestrian as I could find to help me understand what LaGrange points are - using Webb as a teaching tool
What is a Lagrange Point? | NASA Solar System Exploration
Here's the only thing I could understand 20% of on equipotential gravity lines.
Gravitational Potential | Digestible Notes
here's brain-freeze math on equipotential gravity lines resulting from Sun and Earth doing their "space dance" for the past 4 Billion years.
Dunno what LaGrange did to account for the moon. Plus the Earths orbit is NOT perfectly elliptical .. meaning the distance between Earth and Sun varies as Earth completes one orbit. that affects the lines too.
Boil all that down, I think "eddy currents" is a good way imagine all that math. I defer to you, Fratzog, and other folks who wanna "dive in into the well" on this one