1) Put the map .biq file in your "scenarios" folder.
2) Open the map in the Civ3Conquests Editor.
3) Select "Import" from the "Files" dropdown menu.
4) Click "Yes" to proceed.
5) Select "Rules" from the options presented to you next (you don't want Map info or Player info imported to your map, unless the mod/scenario has custom player information -- I don't think LotM does).
6) Then select the Lord of the Mods main biq file to be the source for your imported rules.
7) Save the changes to the biq, once the import has been successful. Now the map will have all the rules of your mod!
8) You may want to reassign all the player starting locations so that Mordor starts in Mordor, Gondor in Gondor, etc. Find each player starting location on the map (assuming that the mapmaker put them there, otherwise put them there yourself as an 'overlay'), and right click on them. Select "Reassign" and then select the nationality you want to start there.
And then away you go!