Can't close my lips naturally. Is this normal even after years with braces? (photos)

I would recommend that you find a doctor who understands oral myofunctional therapy. I would look at your tongue as the major culprit of your inability to close your mouth. Check to make sure that you are not tongue tied. Then you need to improve your tongue position. The tip of your tongue should touch just behind your upper front teeth at rest and the body of your tongue should rest in the roof of your mouth NOT the middle or bottom of your mouth. You should also check your swallowing and make sure there is no facial movement or flexing during swallowing. Your lips should be motionless during swallowing. Also check to make sure you are breathing through your nose and NOT through your mouth. You more than likely need to have some intensive myofunctional therapy. This therapy will help you with your breathing, your tongue position, your swallowing and your lip closure. It will also improve the retention of your orthodontics.Buenas suerte!