Will I be able to keep my lips closed? (Photo)

I am sorry you have found yourself in this predicament.
When crowded teeth are are lined up with out creating space, the front teeth always lean forward.  You are halfway through your plan so consider them halfway forward.  It is going to get worse than just lip incompetence, as they continue to lean outward they can start to appear as a big overbite because your lower lip begins to slip behind the teeth which magnifies the effect of the leaning.
There is another thing to be concerned about.  If the teeth are pushed to far, they can actually be pushed out of the jaw bone and set the stage for significant gum recession in coming years.  I would be particularly concerned about your upper right canine.  
If you are unhappy with the way your treatment is going, I would suggest that you not continue advancing in your trays.  If you are concerned about your gums, see a dentist, or a periodontist (gum specialist).  If you want to undo any negative effects this treatment may have created (either cosmetic or dental health related) see an orthodontist.  If you are upset about being in this situation in the first place, contact your state dental board.

in yr case if IPR is not done thn 2 - 3 mm proclination will occur and teeth will look forward. and that results in incompetent lips. if u will try to close yr lips thn it will change lip size / shape of lips.

I understand your concern and when you have treatment done by a specialist or suitably trained General Dentist, there is always consideration of not only tooth position, smile, but also soft tissue, such as the lips. 
Smile Direct to the best of my knowledge only covers the position of the teeth.  In addition, you are started with a moderate malocclusion and doing treatment on yourself can lead to permanent damage
I would talk to your dentist or an Orthodontist to see where you are at and determine if maybe you should consider professional treatment.