Bring water and barley to a boil in a saucepan. Reduce heat to low, cover, and simmer until barley is tender, about 30 minutes.
Drain any excess water from barley and transfer to a large bowl; stir in 2 tablespoons olive oil.
Heat remaining 1 tablespoon olive oil in a large skillet over medium heat. Add corn; cook and stir until slightly softened, about 2 minutes. Stir in tomatoes and scallions; cook until scallions are wilted, about 2 minutes.
Mix corn mixture into barley in the bowl. Stir in mixed greens, lemon juice, and lemon zest. Season salad with salt and pepper.