Lag/Not Connecting?

So this has been happening for awhile now. Specifically about 4 days. I have been playing league for a few months at both my apartment and my school. At my school, whenever i go to play, whenever champion select ends and it sends me in-game, i get a bugsplat. Every time. I have tried going on custom games and blind picks, and both give the same result. I have tried re logging , reconnecting, repairing files, updating EVERY driver on my laptop, and soon will be resulting to uninstalling and reinstalling. I am not the only one however. Some of my friends also have been getting this issue (we all have the same model laptop as required by the school It is a lenova p40 yoga) and none of us are able to get on. However at the apartments, we all experience extreme lag. We all have godly internet and these laptops are also quite great. I used to be able to run graphics at very high with around 80 fps at all times. Now, my graphics are set to very low, yet I'm getting around 60 fps usually, and seemingly random lag spikes where my fps drops to "20" which is actually around 10 or so. I run other games such as h1z1 or overwatch with no issues. Is there any way to fix this? (The two problems may not be connected but they both happened around the same time so I'm assuming they are connected somehow.) Also i just got a new monitor and when playing on the new monitor it tends to lag, but still connects if that helps.