Ms and fps problems

Ok so whatever i cap my fps on it always goes a little below it. Cap at 60 it goes to 59 , 80 to 79 etc and it somewhat makes me lag at times. The game shouldnt feel laggy at 119 fps but it does sometimes even if the fps doesnt drop. I also used to have like 22 ms a year ago. My internet is still exactly the same ( i have checked it) but now its 39 and sometimes spells get delayed etc. This has made me quit the game, i play like 1 game a month to not drop atm but its not fun with the lagspikes. Why cant i run league with 250 mb/s and gtx1060 8gb ram?