Been having the same issue, was fine from the Preseason update, but today my ping spiked to 800, and I managed to drop it to 300 but that was me by myself in a custom game, atm LOL is unplayable at the momentwith the lag.
I tested my connection, during all this and the test came out fine, also I'm capable of playing any other online game without such ping problems.
I'm almost certain it's an issue on Riot's end because the forums are even laggy for me, while other websites are loading fine.
Also I keep getting firewall warnings, but my League client is being allowed through my firewall, so I don't know what that means