Place the arugula, carrots, and tomatoes in a large bowl.
In a small bowl or large measuring cup, whisk together the dressing ingredients: lemon juice, balsamic vinegar, olive oil, and salt. (Alternatively, you can shake them all together in a mason jar with a tight-fitting lid).
Drizzle enough over the arugula to moisten it, then toss to combine.
Sprinkle Parmesan and any desired nuts or herbs over the top. Serve immediately with a drizzle of extra dressing as desired.