Developing glute strength is a good place to start when looking to decrease lower back pain and stiffness. Weak glutes often lead to poor posture, excessive lumbar extension (lacking the  ability to extend your hips), and injury when performing movements like deadlifts, squats, lunges, etc.
If you are someone who struggles with lower back pain, try performing glute bridges from the floor and holding these for 20 to 30 seconds at a time. As you progress, you can perform hip thrusts with bodyweight and with existential loading, making sure to use the glutes to lift the load rather than simply arching the back.
If you have pain, always consult a doctor before starting an exercise routine.