Rendezvous Math

[Spinward Flow]

the one on Earth-Moon relation is at about 0.45 Mkm. Can you see the difference?

Yes.
L₁ and L₂ of Sol-Terra lie OUTSIDE the 100D jump shadow of Sol AND Terra ... and are therefore usable as jump points (inbound or outbound).
L₁ and L₂ of Luna-Terra lies INSIDE the 100D jump shadow of Terra ... and is therefore "unreachable" as a jump point for inbound, as well as being "highly inadvisable" as a jump point for outbound.

The difference is that these are completely different Lagrange Points for different bodies.
One (Terra L₁ and L₂) are usable, the other (Luna L₁ and L₂) ... not/better not.

Which is the correct way?

Lagrange Points MIGHT be usable as jump points, but it cannot be assumed that they automatically WILL BE in all systems under any and all orbital configurations. At best, Lagrange Points are ... conveniences ... rather than a "freebie" for jump points.

Whatever, as I said, I was wrong in fearing it will be unusable as jump exit point.

Some can, some can't ... it just depends on the details of the star system (and the orbital ephemera tables of where bodies lie in their orbits at specific times).