League of Legends Icon Keeps Bouncing then Disappears [Can't Open the Client]

Okay I need everybody's help because I miss playing league and it's slowly driving me insane. Alright so basically I took a 3 month leave from the game and I just recently decided to start playing again. So as I go to open my LeagueClient it doesn't open [Keep in mind, I have a MacBook Air 2014 Edition that runs a OSX 10.10.5 Yosemite]. My initial decision was to go on the web and re-download the game from scratch. I do that and I get to the part of where it says "Drag the Application to the Applications Folder". As I do that the game replaces the old version and I thought I was ready to start up my client and get patching. BUT NOPE. The game icon starts bouncing for like 20 times on my Mac Docks and it just then randomly disappears. I tried doing the good old "Show Package Contents -> LoL -> delete lockfile". But deleting the lockfile doesn't seem to do the trick. I've also tried double-clicking the LeagueClient tab right above the lockfile, but that doesn't to work as well. I also was contemplating whether I should do a system update and go for the Mac Sierra, although I checked the online requirements for MAC on the League of Legends website and it says that it requires a 10.8.0 or higher 9So i didn't need the update). And also keep in mind that I've been using this computer for the past 4 years and I had absolutely no problemos ever. So at this point I'm completley lost and I don't know what the heck I should do. :(

• I've re-installed the game from the sign-up websites literally like 12 times now, but still no luck. Y'all please try to help me out because I seriously cannot anymore.