Heat vegetable oil in a skillet over medium heat and cook chicken breasts until browned, turning once, about 5 minutes per side. Season chicken with salt and black pepper.
Place asparagus into the prepared baking dish; arrange chicken breasts on top.
Mix cream of chicken soup, mayonnaise, and lemon juice in a bowl; pour over the chicken and asparagus.
Cover the dish with aluminum foil.
Bake in the preheated oven until the sauce is bubbling, the chicken is no longer pink inside, and the juices run clear, about 40 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Uncover the dish and sprinkle with Cheddar cheese; allow to stand until cheese has melted, about 5 minutes, before serving.