Rub cut sides of avocados with 1 teaspoon oil. Rub corn all over with 2 teaspoons oil and sprinkle with½ teaspoon salt and½ teaspoon pepper. Thread shrimp tightly onto four 12-inch metal skewers, alternating direc­tion of heads and tails. Pat shrimp dry with paper towels, then brush with 1 tablespoon oil and sprinkle with¼ teaspoon salt and¼ teaspoon pepper. 

For a charcoal grill: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes. 

For a gas grill: Turn all burners to high; cover; and heat grill until hot, about 15 minutes. Leave all burners on high. 

Clean and oil cooking grate. Grill corn (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. Transfer 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 4 minutes, flipping halfway through grill­ing. Using tongs, slide shrimp off skewers into clean bowl and toss with 1 tablespoon oil and lime zest: set aside. 

Scoop flesh from charred avocado halves and cut into 1-inch pieces. Cut kernels from cobs. Juice limes to yield ¼ cup of juice. Whisk lime juice, remaining 3 tablespoons oil, remaining ¼ teaspoon salt, and remaining ¼ teaspoon pepper together in large bowl. Add romaine, avocado, corn, and shrimp to dressing and toss gently to combine. Season with salt and pepper to taste; serve.