I never touch the textures, they seem to work fine for me with just lowering the actual polys, no retexturing needed. What i do to create complete LOD's for models is the following: (This is working from a single MOD, apologies for it being a bit long)
1. Use "Select By Name" to choose the mod mesh (ignore the hardpoints) such as D5W_1
2. go to "Edit" then "Clone" then "OK" in the box
3. Go back to "Select By Name" and choose D5W_02
4. Go to "Modifiers" then "Mesh Editing" and choose "MultiRes"
5. Hit "Generate" and in the "Vert Count" box choose the new amount of polys (In this case it says 1478 - i set it to 800 for medium range LOD) and hit "Enter" on your keyboard
6. Go to "Edit" then "Clone" then "OK" in the box, this will clone the 800 poly model you just created
7. Go back to "Select By Name" and choose D5W_03 (Should already be selected, but make sure)
8. Hit "Generate" in the MultiRes parameters again and in the "Vert Count" box choose an amount of polys for the long distance LOD (It will say 800 from the previous medium one, set it to 500 in the "Vert Count" box and hit "Enter" on keyboard again
9. Go to "Select By Name" and Select everything, including hardpoints.
10. Now Export as a .MOD in the usual way, choose "No" for "Force Smoothing" and then "YES" for model with multiple levels of detail, in the options box that opens i usually find the default settings are perfectly fine, but make sure "Sort by Complexity" is the option selected (Usually is by default)
And thats it, a method which probably isnt perfect but has always worked reliably for me in creating LOD's for about 2 dozen models and kitbashes now. Sometimes the model may look messed up in the Max Render due to the LOD's, but look at it in ModViewer and it is usually perfectly good with no mesh problems or bleeding or texture glitches. (dont forget you can view the different LODs in ModViewer) No remapping, no retexturing, it all works from the base MOD
And, of course as mentioned above, you dont have to use MultiRes just for LOD's, its useful as hell for lowering the Poly Count of single Meshes and Mods as well, just choose the Mod, select MultiRes, hit "Generate" and enter your new poly count just as i detailed above but without the Cloning stuff.