High Ping to League Only

During the past month or so, I have had issues with my ping in League going up to the 300-400 ms range on occasion. However, I play other games regularly as well (Counter Strike, Dota, etc.) and this issue has never happened with any of those games. Additionally, I have run internet speed tests while experiencing these lag spikes, and the internet speed tests report my latency as being in the 40-60 ms range, rather than 300+.

This is not an isolated issue either, as I have several friends, as well as some guy who I met in a solo/duo game, who have reported exactly the same problem. Is there anything I can do to fix this? It seems to be random, as some games are just fine while others I sit at 350 ping all game. It's been very frustrating recently.