Turning the Corner As an Assassin?

Hey everyone,

Was just hoping for some advice turning a good early/mid game into a good late-game as an assassin. I've had a ton of games where I dominate lane in kills and cs (I mostly play leblanc when I go assassin, so I know it's not hard to dominate lane :p), roam pretty well during laning phase, apply pressure w/ my jungle, and help people grab a few turrets.

But I'm having trouble turning that into being effective mid-late game. I'm in Silver now (Gold last season), and I feel kind of useless when people just ARAM, and 3 tanks/bruisers with cc are constantly stacked on top of their squishies. I would try to split-push, but I don't think LB is particularly strong at that compared to other assassins that like to split and challenge someone to come 1v1 them (zed, talon).

I know the basics: wait for them to burn some cc before going in, prioritize squishies, get sweeper and wait in commonly-traversed areas, etc., but I'm still having a lot of trouble transitioning having a really strong start (even when I help other lanes start strong too) into a solid mid-late game.

Any tips? Thanks!