I'm having the same problem - or a similar one - with some mesh items i'm working at.
Adding a single triangle to the model results in the LOD steps happen in much shorter distances than expected. Like i have to move the camera within 0.1 meters from the prim center to make LOD3 appear (this is with LOD factor setting=1). The size of this model is about 0.4x0.5x8.0 and it is expected to display with LOD3 until quite far away.
After reading this thread i can relate the issue with the fact that these meshes behave ok until they use only two materials... and behave bad after adding even a single triangle that uses a new material.
I tried to browse for the JIRA referenced here but it seems deleted or locked (SH-2837).