Laser shader currently only supports Local and World space.
While that works for most cases, it doesnt work well for Line Renderers. As those generate meshes in runtime by adjusting their vertex positions. This causes the noise to constantly move on the surface of the laser, which might be undesireable.
A solution to this is to use UV space for Line Renderers. As they are, by definition, 2D - the 3rd dimension doesn't matter and UVs can be used without any downsides.