on the router, you can distribute the speed, just do it in half. and you will not return to such difficulties
This is not the issue here. This would maybe be the issue if they both wanted to watch movies on 4K and it started to get choppy for both of them. However mining uses almost no bandwidth.
There are 2 causes for this.
First one is that its a crappy router and when there is more load on the router, the CPU inside the router can't keep up and it ends up slowing down the latency rates.
Second issue is that the LOL player is using Wifi and when the OP is mining there might be some interference from the GPUs, depending on how many he has in his room.
Its most likely one of these issues. I would just tell the LOL player to use an ethernet connection and see if the issue goes away, if it doesn't then get a better router.