How to Make my Lips Touch Naturally

You need to be evaluated by an Oral Surgeon or Craniofacial Plastic Surgeon who specializes in orthognathic surgery. With special X-rays they can analyze what surgery would be best for you. I suspect they will recommend a maxillary shortening procedure (Lefort surgery) to correct this problem. 

I do NOT recommend injection of Botox or releasing the muscles of your upper lip that another surgeon indicated.

The gap between upper and lower lips are fairly large. Release of the muscles of the upper lip should help. You may also try Botox injection. Both of these will limit the movements of the upper lip but will reduce the gap.