In large pot of boiling, salted water, cook potatoes until just tender when pierced with fork, about 15 minutes. Drain and cool slightly.
Slice one lemon into 1/8-inch-thick rounds. In small saucepan, combine sliced lemon, water and kosher salt; bring to boil. Reduce heat and simmer until lemon slices are tender, about 10 minutes. Drain lemons, then coarsely chop.
Cut remaining lemon in half and squeeze out 2 tablespoons juice. In small bowl, mix chopped lemons, lemon juice, white balsamic vinegar and oil.
Coarsely crush cumin and coriander seeds using mortar and pestle. Mix seeds into lemon dressing. Season, to taste, with pepper.
Cut lukewarm potatoes in half lengthwise. Place in large, shallow bowl. Mix in green onions and dill. Pour lemon dressing over and toss to coat. Season, to taste, with salt and pepper.
Add arugula and toss gently. Serve lukewarm or at room temperature.