Dune, I am not sure what you mean by displacement intersection. So I don't think so. And there is a sun. The rocks are just in a shaded area. The sun is low on the left and the rocks and water are down in a depression. So there is a shadow across the pebbled area. Would the shaded area be calculated differently every time by GI, and only when the lake is enabled? It seems like with some of these issues I am having that something to do with GI is the source of the problem. And all my GI settings while doing these tests are the default ones.
Sharing the file is a bit of a problem. It has all sorts of stuff that goes with it that is too big to upload, such as the vector displacement (4096x4096 EXR) that makes the depression where the rock bed is, some OBJs, and so on. There is also a secret in there!

I think that in the morning, I am going to try recreating the file. I had a problem like this before with this scene where my waterfall was black in the shaded area intermittently. Rebuilding the file by creating a new file and bringing my main nodes in with clips files seemed to fix it.
All these problems I am having might just keep me from making the deadline for the contest! *sigh*
I ran processor and memory diagnostics and all was fine.