Can you do a few minutes' worth of streaming attempt with another game (Using your own rtmp server you have set up) using the same OBS streaming settings and configuration as you would for LoL, closing down OBS after you have finished the stream attempt and upload the logfile please, for a comparison stream attempt.
Again, not sure why it would be affecting just one game in particular, especially with ~40% dropped frames due to bandwidth issues.
https://gist.github.com/anonymous/2b370ace06cb3445816aaa6a088cc3f0
In this one I had played shadowverse for 10 mins and league for 40 mins.
I had closed OBS after streamed.
Its should record the infos you wanted.
Thanks.