My bet's on the meta becoming assassin and ADC centric after a few outlier champions (Mundo) are nerfed.
Right now ADC itemisation is actually insane, and the LW upgrades are getting buffed, dispite the fact that Lord Dominik's deals more damage against tanky champs than old LW ever did. There's going to be no reason to play tanky champs once this happens, duel ADC teams will be picked up to melt tanks whenever they're picked, since they'll be able to melt through the tank in a matter of seconds. If you're wondering how you run multiple ADCs Ez and Corki have historically been played mid, in theory the new Graves and Lucian can also work.
With tanks flat out not being able to answer ADCs most mid and top laners as well as junglers will move to the next best possible answer, assassins. I'd expect to see huge hikes in the play rates of assassins and assassin like bruisers and mages.
Top lane will probably shift to champs like Irelia, Fiora and Quinn. Poppy is also a possible competitive top laner since she has reasonable anti ADC traits and specifically counters the incoming assassins, even although she doesn't have very many assassin like traits herself.
Mid will most likely shift towards champs like Ekko, Zed, Dianna, LB and Talon. It mostly be dominated by true assassins, but there's room for specific mages to see play as well. Azir would be my top prediction, since once again he has specific anti assassin traits and he also is a fairly strong lane counter to most melees, which most assassins are.
Jungle will be the standard shit it devolves into when tanks aren't particularly good. Lee, Nidalee, Rengar and probably some of Eve, Rek'sai, Elise and J4. I don't think that this on needs to be overly justified, it's pretty much just what happens when Riot screws around with the jungle and does something stupid like splitting the starting jungle item into two.
Basically I'm predicting a complete shitfest meta, because the last time I saw Riot have a heavy emphasis on diversifying AD items was at the start of season 3 and I can only make predictions based off of what I've already seen.