Rub cut sides of avocados with 1 teaspoon olive oil. Rub corn all over with 2 teaspoons oil and sprinkle with ½ teaspoon salt and ½ teaspoon pepper. Pat shrimp dry with paper towels then toss with 1 tablespoon oil, ¼ teaspoon salt, and ¼ teaspoon pepper. Thread shrimp tightly onto four 12-inch metal skewers and tightly pack (6 to 8 shrimp per skewer), alternating direction of each shrimp. 

Grill corn over hot fire (covered if using gas) until charred on all sides, 10 to 13 minutes, turning as needed; transfer to cutting board. Grill avocados and lime halves (covered if using gas), cut sides down, until lightly charred, about 2 minutes; add to cutting board with corn and let cool slightly, about 5 minutes. 

Meanwhile, grill shrimp (covered if using gas) until lightly charred and opaque throughout, about 2 minutes per side. Using tongs, slide shrimp off skewers into clean bowl and toss with 1 tablespoon oil and lime zest; set aside. 

Using spoon, scoop avocado flesh from skin and cut into 1-inch pieces. Cut kernels from cob. Juice limes to yield ¼ cup. Whisk lime juice, 3 tablespoons olive oil, ¼ teaspoon salt, and ¼ teaspoon pepper together in large bowl. Add romaine, avocado, corn, and shrimp and toss gently to combine. Season with salt and pepper to taste and serve.