Add the shrimp, 2 tablespoons olive oil, lime juice, lime zest, and kosher salt to a large bowl and toss to combine. Cover and refrigerate for 15 minutes.
Once marinated, heat a large skillet over medium heat and add the remaining tablespoon of olive oil. Add the shrimp, making sure to put them all in a single layer.
Place 3 shrimp in the center of the rice paper. Add a piece of butter lettuce, a few sticks of carrot, a piece of cucumber, a slice of avocado, a few green onions, and two herb leaves on top.
Roll the summer rolls the same way you would a burrito– by folding the bottom over the toppings, folding the sides in, and then rolling upward to seal.