We like to top this salad with a fried egg, but you could swap in a poached or soft-boiled egg, or even an omelet, if you prefer.
Cover potatoes with 2 inches of water in a pot and bring to a boil; add salt. Cook until potatoes are easily pierced with the tip of a sharp knife, about 10 minutes. Remove with a slotted spoon. Add snap peas and asparagus to pot, and boil until crisp-tender, about 2 minutes; drain. Slice potatoes into 1/4-inch-thick rounds.
Melt butter in a saucepan. Remove from heat and whisk in lemon juice and sugar; season with salt and pepper. Divide lettuce and vegetables among 4 plates. Drizzle with warm dressing, and top each with an egg. Season with salt and pepper; sprinkle with chives.