Bring some water to the 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 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 flavours to blend; about 1 hour. Drizzle lime juice over salad; toss gently until combined.