LOD groups and textures?

When making a LOD group, should each LOD have its own texture with increasingly lowered resolution, or will mipmaps allow all LODs to use the full resolution texture at no performance cost?

Since a LOD group consists of very different 3D meshes you want to bake textures and normal maps for them all from the highest poly count model and highest resolution texture, so there will be separate textures for each.

You want to keep the textures high res though, unless you’re really trying to optimize for performance, since the texture quality can be downscaled separately in the Quality Settings (Edit → Project Settings → Quality). That way, you could create a Quality Setting for “low poly + high res” or “high poly + low res” if you wanted, and any other combination.