Lagrange points

The movement of Lagrange points through outer space is simulated:

https://simulations4all.com/simulations/lagrange-points

And from NASA:

https://www.nesdis.noaa.gov/our-satellites/lagrange-points-orbital-parking-spot-...

Wolfram-Alpha has various diagrams and discussions:

https://www.wolframalpha.com/input?i=Lagrange+points+Earth+and+Moon