Heat a Dutch oven or large skillet over medium heat. Add bacon and fry, stirring occasionally, until bacon is crisp, 5 to 7 minutes. Transfer bacon to a paper towel-lined plate.
Drain all but 1 Tbsp / 15 mL of bacon grease out of the pan. Return pan to medium heat.
To heated pan, add chicken. Sear chicken on both sides until cooked through, 5 to 7 minutes. Set chicken aside, covered to keep warm.
To heated pan, add butter and then green beans and asparagus. Saute for 2 minutes to get vegetables started cooking. Add water and then cover with a lid. Steam vegetables, covered, until tender, 4 to 5 minutes more. Season vegetables generously with some salt and squeeze lemon juice over top.
Spoon pesto over chicken and top with crumbled bacon. Enjoy vegetables on the side.