The two are completely separated concepts.
LOD (Level-Of-Detail) is related to a mesh ora a material. Depending how far an object is, or how small the object is in percentage of the screen, the proper LOD level of a mesh (or/and the material) is selected. You could not have LOD for meshes and materials, it’s up to you.
Mipmaps are only for textures. Is a way to reduce the minification-magnification issue that happens when the pixels of the render don’t really match in size with the texels (the pixels of the texture). I’ve explained this in a very few words, check for example here to know more. This is not really related to how close you are to the camera, but it depends of the texel ratio to screen. Mipmaps are computed by the graphic API, and if the texture is a power of two, the mipmap chain is more efficiently generated.