Whisk mayonnaise, sour cream, and lemon juice in small bowl to blend. Stir in chopped eggs, capers, parsley, tarragon, and shallot. Season sauce to taste with salt and pepper. DO AHEAD Can be made 1 day ahead. Cover and refrigerate. Cut off bottom 1 inch from each asparagus spear. Using vegetable peeler, peel each spear from about 2 inches below tip to base to remove stringy outer layer. Bring large saucepan of salted water to boil. Squeeze juice from 1/2 lemon into boiling water; add lemon half, butter, and sugar. Add asparagus and cook just until tender when pierced with knife or skewer, 5 to 8 minutes, depending on thickness and color. Using slotted spoon or tongs, remove asparagus from saucepan and transfer to platter to cool. DO AHEAD Can be made 1 day ahead. Cover; chill. Just before serving, add 3 tablespoons olive oil to sauce and stir without overmixing (sauce should have coarse texture and olive oil should be slightly separated). Arrange asparagus decoratively on platter or individual plates. Drape salmon slices over. Spoon a few tablespoons sauce over; drizzle lightly with additional olive oil. Serve, passing remaining sauce alongside.