Using a meat tenderizer, pound chicken breasts to an even thickness.
Whisk together lemon juice, garlic, herbs, salt, pepper, and 3 tablespoons of the olive oil. Marinate chicken and mixture in airtight container or resealable bag for at least 30 minutes and up to 2 hours.
Place 2 teaspoons olive oil in a skillet over medium-high heat. Spread oil and coat the pan. Add chicken. Cook for 1 minute on each side. Flip breasts again and reduce heat to low.
Cover pan with a tight-fitting lid. Cook for 10 minutes (check time). Do not remove lid while cooking. After 10 minutes, remove pan from heat, still covered, and allow to sit for 10 additional minutes.
Make sure there is no pink in the middle of the breasts or that a meat thermometer reads 165 F when inserted in the center.
Meanwhile, for Asparagus
Preheat oven to 400 degrees F.
Toss asparagus in olive oil, salt, and pepper. Spread on a sheet tray. Roast for 18-20 minutes, flipping asparagus halfway through until slightly browned and tender.
Toss greens and tomatoes together. Toss with a vinaigrette of choice or serve the dressing on the side.