Cook the farro as the label directs. Drain and rinse under cold water, then transfer to a large bowl and toss with 2 tablespoons olive oil.
Heat the remaining 1 tablespoon olive oil in a large skillet over medium-high heat. Add the corn and cook, stirring occasionally, until it begins to char, about 2 minutes. Add the tomatoes and scallions and cook, stirring, until they just begin to wilt, about 2 more minutes. Add 1/4 teaspoon salt, and pepper to taste.
Stir the corn mixture into the farro. Add the arugula, lemon zest and lemon juice and toss. Season with salt and pepper.