What to do when you're ahead in lane and you've already taken down the t1 turret? For any lane?

Just something I noticed last game. I was playing in the mid lane and I crushed the enemy , but after I took down the first turret, I didn't know what else to do. I pushed up to the second turret, but you can't stay to siege it or you'll get ganked right? Unless you have vision of the whole enemy team.

So I pretty much hung around bot lane until a fight broke out in the river, I prevented the Sona and Vayne on the enemy team from joining the fight, and we won that fight overall. And I basically returned mid to push to the second turret and then went back bot lane or basically with my bot laners and/or jungler to see if we could make a pick or something. Rinse and repeat. I feel like I'm missing something.

So, any tips?