Do you live in a town/city, or rurally? Do you use a wired or wireless connection? Do you have multiple family members utilizing the Internet throughout the day on the same connection as you? What times do you normally play League?
If you live rurally, the likely issue is the same as mine; you get your Internet connection from a satellite, rather than cables underground. From what I've been told (and from some research I've done), air traffic from other people near you also using the same satellite (or even people using cellular data on their phones) becomes jammed during certain times of the day. This happens to everyone I know, even if they DO get their connection with cables, but I know that this problem is exacerbated when you live rurally like myself. I would recommend an ethernet cord if the problem is inconsistency (so, instead of your ping being anywhere from 65-70, it's now anywhere from 65-150 in an unpredictable pattern). Even though League uses a small amount of bandwidth, like I said (and especially if you are rural), if you're family is on the Internet while you are on it, more air traffic, which means higher ping values...and typically spikes as well. You might want to play League after your family is done using the Internet if you want to have few spikes/inconsistencies in your ping.