I don’t have enough expertise to give you a definitive answer, but I think you don’t fully understand how Lagrange points work. Mind you, I’m not sure I understand how they work, either, so what I’m about to say may be worthless. So keep some salt handy.

A Lagrange point is a place relative to the orbit of the satellite object where the gravity of the satellite and its primary cancel out. Any third object that somehow wanders into one of these points tends to stay there because of the gravitational interaction between it, the satellite and the primary.

So there are Lagrange points relative to the Earth and the Sun where the gravity of both cancel out. The JWST is stationed at one of these points now. Saves JSWT a lot of fuel for station keeping.

There are Lagrange points relative to the Moon’s orbit where the gravity of the Earth and the Moon cancel out as well. We’ve placed nothing there yet but that could change one day.

The deal with Lagrange points is that any third object that somehow makes it’s way to the location of one of the Lagrange points tends to stay there. This happens with small objects such as spacecraft or asteroids floating around the solar system because they don’t have much mass relative to the Earth or the Moon to affect the location of the Lagrange Point.

Now let’s consider a planet.

Planets are much bigger objects. Everything in a planetary disk starts out orbiting the star. Objects collide with each other frequently. The thing is these objects are not initially in any Lagrange points. They approach and each attracts the other. The Lagrange points aren’t likely to be along the vector of approach and there’s a lot of force pulling them together. As they get nearer, the location of the Lagrange points change because of the large amounts of mass approaching each other. If they collide, after all, there would be a lot more mass where the original planet was, changing where the Lagrange points are; the same thing happens when the 2 planets are closing in on each other.

So planets, because they’re so big, will orbit each other or collide. I don’t see how they could be in each other’s Lagrange points.

The Lagrange point sets the mass of the third body to zero before solving the differential equation.