Butter-Lettuce Salad with Egg and Potatoes

Name: Butter-Lettuce Salad with Egg and Potatoes
Prep time: 40 min
Total time: 40 min
Cuisine: European
Ingredients: 1 pound baby (golf-ball-size) potatoes; Coarse salt and freshly ground pepper; 8 ounces sugar snap peas, trimmed and halved on the bias; 1 pound white or green asparagus (peeled, if white), tough stems trimmed, cut into 2-inch pieces; 1 stick unsalted butter; 2 tablespoons fresh lemon juice (from 1 lemon); 0.25 teaspoon sugar; 1 to 2 heads butter lettuce, such as Boston or Bibb, leaves separated, large ones torn into 2-inch pieces (about 12 ounces); 4 large eggs, fried; 0.25 cup snipped fresh chives (from 1 bunch), for serving