Place chicken between 2 sheets of heavy plastic on a solid, level surface. Firmly pound chicken with the smooth side of a meat mallet to a your desired thickness. Season with salt and pepper. Place chicken in a baking pan.
Combine 3/4 of the lemon juice, onion, 1/4 cup olive oil, garlic, and oregano in a bowl. Pour marinade over the chicken.
Heat 1 tablespoon olive oil in a saucepan over medium-high heat. Saute tomatoes for 3 minutes. Add spinach; season with salt and remaining lemon juice. Cook and stir until spinach is slightly wilted, 1 to 2 minutes. Pour over the chicken in the pan. Sprinkle feta cheese on top.
Bake in the preheated oven until chicken is no longer pink in the center 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).