Place 1 inch of water in a 4-quart pot with a lid. Place a steamer basket inside the pot, and add asparagus. Cover and bring to a boil over high heat. Reduce heat to medium. Cook for 5–10 minutes, until asparagus is easily pierced with a sharp knife. Do not overcook.
While the asparagus cooks, grate the lemon zest into a small bowl. Cut the lemon in half and squeeze the juice into the bowl. Use the back of a spoon to press out extra juice and remove pits. Add mayonnaise, parsley, pepper, and salt. Stir well. Set aside.
When the asparagus is tender, remove the pot from the heat. Place asparagus spears in a serving bowl. Drizzle the lemon sauce evenly over the asparagus (about 1-1/2 teaspoons per portion) and serve.