My Lips Don't Close Naturally, What Can I Do? (photo)

I can see your concern but to answer it may be difficult based on what is presented.  Looking at your photographs, it appears that your facial type would be in the "longer" facial type zone compared to the "square jaw" facial type at the opposite end of the spectrum.  Your lower jaw is not prominent but goes along with this facial type.  I find that relaxed lip closure is often a problem in these cases.  We will extract teeth to be able to reduce the facial fullness of the dental arches while fearing too much loss of facial support will be undesirable.  In your case, further retraction of your front teeth may result in too flat a profile but would allow your lips to be more relaxed....maybe.  The chin strain I see in your "lips closed" photo leads me to think that you may be in this limbo area.  Here is a trick I have used on open mouth cases with mixed results, but it can not hurt to try:  This sounds stupid but ......  Get a large flat button and slide it on a long piece of string making a low-hanging necklace.  Hold the button lightly between your lips.  If it falls down....pick it up and put it back between your lips.  This can train your lips to be closed while strengthening them.  Do this exercise for several hours a day.  You may be pleasantly surprised!  Good Luck!