Wash arugula and lettuce and let dry on both sides on paper towels.
Trim off the bottom 2 inches of the asparagus and place in a bowl of cold water to clean. (Peel the spears if you're using white asparagus.) Bring lightly salted water to a boil in a 2-quart saucepan. Cook asparagus for 2 to 3 minutes and remove to an ice water bath. When cold, remove and drain on an absorbent cloth.
Cook peas in the same water once it returns to a boil, about 6 to 8 minutes, and remove to an ice water bath. When cold, remove and drain on an absorbent cloth. Repeat with fennel bulbs, cooking until a little firm. When cold, cut into wedges.
Wash radishes, slice as thinly as possible and place in a bowl of ice water until you are ready to use. Trim onions and slice very thinly.
Meanwhile, prepare vinaigrette by whisking together lemon juice and olive oil.
Place arugula, lettuce, radishes and onions in a bowl and add 2 tbsp. vinaigrette, a pinch of sea salt and a few turns of black pepper. Gently toss to lightly dress greens. Season and brush cooked asparagus, peas and fennel with vinaigrette. Arrange salad on plates.