There are programs out there that can slow down a process (changing priority will only change the relation between processes, so if only League uses 90% but all other processes use 0-1%, League will continue to use 90% of the CPU).
If you want to go "vanilla" you can only try to make League as "light" as possible by capping the FPS at 25 (the ingame settings do not allow less) and setting the lowest possible settings etc, however this is not what these bots do.
The bots themselves do not require much CPU as they do not scan pixels every frame, rather 3-4 times per second (less CPU intense), they run League on a reduced window size so they need to scan less pixels but they also slow League down (this will reduce the fps as well). FPS limiters (judging from my experience) do not help much.
I found a program which does slow the game down to use roughly 30-40% CPU (Translates to roughly 6-8% CPU on main PC, depending on processor).

It could be that these bots limit the CPU-time of League in a similar way. I could only limit as much as 60% of League, anything higher caused frequent crashes during the loading screen.
Another way is to customize the virtual machine (some commercial pixel bots come with their own optimized virtual machine) to use less CPU and have as few background processes as possible, no windows-bloat etc...
The slower game would also explain why these bots always "toast" the loading screen when you have them on your team, their game just runs so much slower.