Tanky Lee Sin is all about macro strategy. You can still be thirsty for kills early game, sure, but what's really important is that you immediately turn these kills into objectives. A gank on bot lane MUST turn into a tower or dragon if the ADC is healthy enough for it. Power shove mid and open them up to roam, or get them to help you take an objective if they are AD. Blow the enemy top laner's summoners so you isolate them to that lane in particular and stop them from teleporting down to assist their allies. Occasionally countergank or counter jungle the enemy Jungler so you maintain a level (and thus Smite) advantage over them. Every kill based action must snowball into a bigger objective based action. That's how you win games, especially with champions like Lee Sin who can potentially dominate the early game.
Get some CDR on your build and cater your mid to late game playstyle into all about forcing bad fights for the enemy. If you know how to insec, you should basically never allow the enemy carry to be in a safe position. Exactly how you engage depends on the enemy team comp and you should probably learn this out of experience rather than me feeding you info, but the idea is there; isolate the enemy carry, force them out of position with an insec or kick flash, and force bad fights for the enemy team.