Bring water to a boil in a saucepan. Add asparagus; boil for 1 minute. Add snow peas to asparagus, boil for 1 minute more. Drain and pat dry.
Transfer asparagus and snow peas to a large bowl. Add radishes, scallions, and dill; toss salad gently to combine.
Whisk oil, sugar, salt, and pepper together in a small bowl; pour over salad and toss to coat. Set aside at room temperature to allow flavors to blend; about 1 hour. Drizzle lime juice over salad; toss gently until combined.
Some or all of the green asparagus can be substituted with white asparagus, if desired.
Salad can be set aside in refrigerator instead of at room temperature to allow flavors to blend, if desired, by refrigerating for at least 3 hours and letting stand at room temperature for 30 minutes before serving.