You are still lagging and skipping frames, in League of all games, with a 1080ti. Battlefield 5 I can understand, but not League, League does not use 99% GPU nor 80% CPU

19:49:45.764: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 262 (0.9%)
19:49:45.765: Video stopped, number of skipped frames due to encoding lag: 82/29182 (0.3%)

You are below 1% but you are doing x264 Very Fast 720p60, you should not be having these issues. Only thing left is the camera, unplug it

And don't have your stream open in Chrome/Firefox
At this point I am going to suggest you use NVENC, I don't know how you are having Skipped Frames playing LoL doing Very Fast, but NVENC will solve your encoding issues. For your lagged frames, you have already Disabled Game Mode, you may need to cap your FPS to reduce GPU usage

NVENC quality on a 1080ti is equivilent to x264 Very Fast/Faster.

Something has changed that is not immediately apparent in your logs, the only thing that is clear is your 7700K is not performing how it should for 720p60 Very Fast. Very fast is...very easy for even a 4/8t CPU.

11:17:55.943: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 904 (0.7%)
11:17:55.948: Video stopped, number of skipped frames due to encoding lag: 9702/122498 (7.9%)
I've been reading a lot about these issues in OBS/SLOBS but no one is talking about Windows Updates being the cause.

I've been having the same issues with CPU usage in OBS while streaming BUT NEVER had any problem BEFORE the Windows Updates from November/December. Everything was running perfectly fine before but here we are messing up in OBS (settings, scenes collection...), with the drivers, the updates and some even formatted their computer just to end up in the same exact state.

I'm sorry but while some people might have issues for complete different reasons, I feel like some like me had a good working setup that got screwed by some Windows Updates impacting resources usage such as the CPU in OBS or any other program.

Although a lot of the proposed solutions might work for some, a lot are closing their eyes to more simple explanation such as "how about everything was fine but got screwed by Windows Updates and now we have to wait until Microsoft decides to properly update Windows and fix their previous updates".
Yeah that's exactly how I feel I ended up just lowering some settings, capped fps at 48, and lowered webcsn quality.
I have tried to troubleshoot the problem as much as I could with many approaches but ultimately I really believe it has to do with Windows and its updates. My stream was running smoothly BEFORE the Win updates, after is another story and at that moment, the only thing that changed in my system was Windows and the updates it installed.

Since then, I've tried so many things like reinstalling almost everything, rolling back drivers for stable versions, changed my OBS settings a thousand times, turned off things here and there in Windows, cleaned the PC... I mean at some point there's just nothing we can do except waiting for a hopefully more reliable Windows update to fix what they broke.