In a medium saucepan, combine the barley, 3 cups water and 1/4 teaspoon salt and bring to a boil. Reduce heat and simmer, covered, until the barley is tender, 20 to 25 minutes. Drain off any remaining water in the pan and transfer the barley to a large bowl.
Meanwhile, heat the oil in a medium skillet over medium heat. Add the leeks, season with 1/4 teaspoon each salt and pepper and cook, stirring occasionally, until tender, 7 to 8 minutes. Add the peas and lemon zest and cook, stirring occasionally, until heated through, about 3 minutes; stir in the parsley. Fold the mixture into the barley.