Can a Lagrange point move relative to other forces acting on it

In this recently asked question on a large, sun blocking object it is pointed out in the comments that there would be ~10e7 N of thrust from the sun due to solar wind.

My question is does there exist a point, similar to the sun-Earth Lagrange point, where the gravitational and the solar wind forces will cancel out and so the described object would remain stationary without the need for any (or at least very little) maintained thrust?

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Can a Lagrange point move relative to other forces acting on it

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