Bring a large pot of salted water to a boil. Add the potatoes and cook until just tender when pierced with fork, about 15 minutes. Drain, return the potatoes to the pot (off the heat), and let cool slightly.
Slice 1 lemon into ⅛-inch-thick rounds. Add the lemon slices to a small saucepan with the 2 cups water and kosher salt. Bring it to a boil. Reduce the heat and simmer until the lemon slices are tender, about 10 minutes. Drain the lemons and coarsely chopthem.
Cut the remaining lemon in half and squeeze out 2 tablespoons of lemon juice. In a small bowl, whisk together the chopped lemons, lemon juice, white balsamic vinegar, and oil.
Coarsely crush cumin and coriander seeds using mortar and pestle or by pulsing them in a spice grinder. Stir the into the lemon dressing and season with the pepper.
Cut the lukewarm potatoes in half lengthwise and put them in a large, shallow bowl. Add the green onions and dill and stir to combine. Pour on the lemon dressing and toss to coat.
Season the potato salad with salt and pepper. Add the arugula and toss gently to combine.
Serve lukewarm or at room temperature.
Recipe by Go Dairy Free at https://www.godairyfree.org/recipes/fingerling-potato-salad