I was having the same issue a few weeks ago. I noticed that the lag spikes did not occur during Dominion, only Summoner's Rift. (note- I did not try TT) I tried a few things: updated all drivers, uninstalled and reinstalled LoL, and tried 3 different computers. I then pulled out an old Netgear router and plugged it in instead of the Linksys I was using. I haven't had any issues since. Not caring enough to troubleshoot the Linksys router, I've left the Netgear plugged in.
I have serious doubts about this resolving other people's issues, but it would be interesting to see what the common denominator is. I ruled out different hardware and software configurations with my 3 computers so the only thing I could think of was the router. Either that, or the issue is on Riot's end.