Bring a large pot of salted water to a boil over high heat. Add the spaghetti and cook until it is al dente. Drain the pasta, reserving 1 tablespoon of the water.
While the pasta is cooking, heat the olive oil over medium-high heat. Add the tomatoes and cook for 2 minutes, stirring. Add the arugula and cook for 2 minutes longer, stirring.
Add the pasta, salmon, reserved water, and lemon juice to the pan, and season with salt and pepper. Gently mix until combined.
Transfer the pasta to individual plates. Arrange some arugula over the top and drizzle with a little olive oil. Serve immediately.