Bring a large pot of water to a boil. Add snap peas; cook for 2 minutes. Drain and rinse under cold water. Set aside.
Crush 1-1/2 tablespoons of the raspberries through a strainer into a bowl. Discard pulp. Whisk olive oil, vinegar, salt, pepper and sugar into strained juice.
In large bowl, toss dressing with snap peas, remaining raspberries, blueberries, walnuts and lemon juice. Cover and chill for 30 minutes. Toss with greens and serve.