The LOD filter can improve optimization by reducing memory bandwidth usage and ensuring appropriate texture sampling, which can reduce the workload on the GPU. However, the overall impact on performance will depend on the specific use case and the complexity of the shaders being used.
In case of CopperCube, I believe the performance would be of negligible amount, as the shader doesn’t automatically adjust the mipmap levels based on the camera distance. It can be used as helper function, and mostly helpful where you want to create low res game in the old PS2 style, so use this shader to change the mipmap levels.