The materials darken around the edge face in the vertical direction of the mesh but I would like these edges to be viewed as seamless. Maybe that is not an option since they are two separate meshes butted right up next to one another.
The best way would be to just use a seamless texture -> either download one or create it by yourself ?v=O7XCEFSjRF8 
I dont know how your texture looks like, but it could be that those seams are caused by a light problem -> do you get any warnings when you rebuild the light? (://www.worldofleveldesign/categories/udk/udk-lightmaps-05-common-problems-solutions.php)
Also, you need to increase the lightmap resolution and make sure that no part of the wall is visible on the outside, otherwise that part of the mesh will be lit by the sunlight and it can bleed across the lightmap to the interior.
Yeah make sure your textures are seamless and tile-able for things like that. It appears the darker edge is baked into the texture here. You’ll have to make sure they wrap on the UVs in proper places to repeat, since they’re on Meshes. Because they’re just right angled walls, fairly straightforward, you can use BSP brushes instead of meshes, and you can manually adjust the materials ( if using a seamless, tile-able texture ) to get the fine tuning just right.