For the dressing, whisk soya sauce, rice vinegar, lemon juice and sesame oil in a small bowl. Whisk in vegetable oil, then stir in spring onion and ginger.
Cook the snow peas in a large saucepan of lightly salted boiling water until crisp-tender, 2 to 3 minutes. Transfer to a colander with a slotted spoon. Rinse under cold running water.
Add asparagus to the boiling water in the saucepan. Cook until crisp-tender, 3 to 4 minutes. Drain in the colander. Rinse under cold running water. Toss snow peas and asparagus in a large bowl with just enough dressing to lightly coat.
Arrange 3 or 4 romaine leaves on each serving plate. Top with snow peas, asparagus and tomato. Garnish with walnuts. Pass remaining dressing separately.