For the dressing: In a small bowl, whisk together the olive oil, lemon juice, lemon zest, salt, and pepper until smooth. Set aside.
For the pasta: Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, 8 to 10 minutes. Drain and reserve about 1 cup of the pasta water.
In a high-sided skillet, whisk the butter over medium heat until melted. Simmer until foamy. Continue to cook until the butter has a nutty aroma and turns a caramel color, 3 to 5 minutes. Remove the pan from the heat. Add the pasta, dressing, arugula, tomatoes, Parmesan, pine nuts, and capers. Toss until coated, adding the reserved pasta water, 1 tablespoon at a time to loosen the sauce, if needed. Transfer to a large bowl and serve.
To toast the pine nuts, arrange in a single layer on a baking sheet. Bake in a preheated 350 degrees F oven until lightly toasted, 6 to 8 minutes. Cool completely before using.