This is not being caused by any of the LushLOD Tree shaders, or by the LushLOD post processing effects. If you disable the post processor, and you switch the billboards to use one of Unity's built-in alpha cutout shaders, the glitch still appears. Changing the Aniso Level of the atlas texture from 1 to 0 makes the line appear worse, and turning on or off Unity's Anti-Aliasing in the project settings can make the line appear more pronounced.
The issue appears to be that this version of Unity (5.5.0f3) is not handling the edges of the UV correctly, and pixels above and below are bleeding into the image. I don't see this happening in version 5.4 of Unity, so I think this is a new issue. I tried editing the atlas image, and deleting the trees that appear above and below this particular tree, and the lines went away. However, I had to delete an excessively large amount above and below to get the line to fully disappear. It wasn't just a few pixels I had to delete. I had to erase like 50 or 100 pixels above and below, to full erase these lines. I pretty confident that my UV's are positioned correctly, so this seems like a bug in Unity.
I'm going to guess that Unity will fix this issue soon, and so for now I'm just going to wait and see if this problem goes away in a later version of Unity.
Customer support service by UserEcho