I am having the same issue. My specs include 2x xeon e5-2680's (2.8gz) 20 core 40 threads and my GPU is a 1080ti.
So I think I have the GPU and enough CPU, but regardless, game runs smooth around 48 fps (GTA 5 Ultra) but obs lags and dips to 20-25. The pattern is random, happens for 10-20 minutes and then usually goes back to normal.
I have tried various recommended settings for obs utilizing either CPU or GPU and I find no solution while the lag spikes are happening except to wait it out. I just wish I knew what it was that was causing the problem specifically, if it is my CPU or GPU.
I will upload the status report file tonight when i get home. I didn't know about that until I found this forum. Thank you all for your time.