I am not sure that I am understanding your question correctly, so please tell me if I'm not. I believe that you want to make an incline with the selected mesh, but instead of an incline, you currently have a sharp drop off.
Why bother with LOD? Why not just go into Edit Mode?
If you go select the last cube and go into edit mode, you can select the two faces nearest to the 3 other meshes on the side and bring them down to the right level. To do this, I keyed G, then Z, then -1. LeftMouseButton to confirm.
If you want to get fancier, you can select the entire mesh in Edit Mode by keying A once or twice until everything's selected. Then you can key W and select Subdivide. Do this twice.
Select the 32 faces that now make up the previously selected two sides of the mesh. Key O to turn on Proportional editing. Key G, then scroll to make the white circle bigger (do not confirm). Finish up with Z, then -1. Now use the LeftMouseButton to confirm.
Tab to reenter Object Mode. Whatever values you were using in your Subdivision surface object modifier for View: and Render:, subtract two. This method takes longer, but it gives the slope a gradient.
The original vid of this setup was too long, so I split it into four parts. Part one:
Here is the final result after Way 1:
Here is a .blend file with both ways in it: