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?
Way 1
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.

Way 2
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:

Part two:

Part three:

Part four:

Final Notes
Here is the final result after Way 1:

Way 2:

Here is a .blend file with both ways in it:
