Bring a large pot of salted water to a boil. Cook the asparagus until tender, about 4 minutes; drain.
Meanwhile, in a bowl, whisk together 3 tablespoons oil, 1 tablespoon lemon juice, mustard, shallot, ¼ teaspoon salt, and 1/8 teaspoon pepper. Toss with the asparagus; set aside.
Heat the butter and remaining oil in a nonstick skillet over medium heat.
Season pork with 1 teaspoon salt and ¼ teaspoon pepper. Cook until lightly browned and cooked through, 1 to 2 minutes per side. Remove from pan.
Add chicken broth to pan and simmer, scraping up brown bits with a wooden spoon, until slightly thickened, about 5 minutes.
Remove pan from heat. Stir in the remaining lemon juice and ½ teaspoon salt. Drizzle the meat with pan juices and sprinkle with zest. Serve with the asparagus.