What is the effect of ordering a jump tender to stabilize a Lagrange point? Intrasystem transit between LPs?
Yes. Ships can move instantly between LPs. They will auto-route between them, so you don't need to do it manually, either.
Note that planets can only have one LP in practice(60 degrees ahead of the planet in its orbit, or the L4 point if you know your orbital mechanics). You can set up multiples for a planet, but they'll all be in the same place, so it's a waste of effort.