Melt the butter in a large oven-safe Dutch oven or pan. Add the thyme and shallots; sauté for 5 minutes. Add the carrots and celery; sauté for 5 minutes. Add the flour; sauté for 1-2 minutes. Slowly and gradually, add the milk and the chicken broth, stirring constantly. Add chicken and peas. Season with salt, pepper, and lemon juice.
Arrange biscuits on top of filling. Bake for 15-20 minutes, until hot, bubbly, and biscuits are cooked through. Serve hot.