Place the diced potatoes in a pot of water. Bring to a boil, reduce heat to medium, and simmer until fork tender but still slightly firm, about 10 mins. Drain and let cool.
Make the dressing by mixing the sour cream, mayonnaise, lemon juice, lemon zest, mustard, salt, and pepper until well combined.
Place the cooled potatoes, red onions, green onions, pickles, celery, parsley, and dill in a large salad bowl.
Drizzle the dressing over the veggies and toss to combine.