I have the same issue, and like the OP, the first time I experienced it was around 8.xx, and after a patch it was resolved. I have experienced this issue again during EVERY game of League that I play, only while playing League since the Akali patch. I've watched it and it always starts around 7-8 minutes into the game. After the issue starts, it repeats roughly every 15 - 20 seconds. The issue is a total freeze of the screen for approximately 1.5 seconds, and any inputs prior to the freeze appear to carried out. I.e. if I clicked to a movement spot, and then the screen freezes, after the duration of the freeze my character is at the location clicked.
I don't have an MSI computer and I don't have a process named anything like "NAHIMIC".
i7-3770k, 1080 gtx ti, 16 gb of ram, all SSD storage. No issues with any other game, I play DCS at max values with Occulus Rift which is far more taxing on my PC than League.
About to update my Nvidia driver to see if this resolves it:
Currently @ Nvidia Driver Version 388.59 12/07/17
Installing Nvidia Driver Version 398.82 8/01/2018.
Ok, after installing the newer driver there's no difference. I still have the same issue, but this time I REALLY paid attention to the screen freezes. Starts EXACTLY 7:01 mins into the game, and on the dot, every 30 secs the issue happens. So, 7:31, 8:01, 9:31, 10:01, 10:31, etc. My initial observations I didn't pay attention as closely and estimated it to be every 15-20 seconds.
Going to bed for the night, but if you believe it's a process issue then it shouldn't be hard to capture with a process capture. I'll look at that tomorrow.
Link to TaskMgr process list:
https://imgur.com/4WYYV4k