How can I reduce fat (or muscle) deposits under my lower lip? (photo)

Marina.  On the one hand, you would be a good candidate for conservative upper and lower lip augmentation. However, this would not affect the line that you are describing below your lower lip. This should be able to be improved with the same fillers for your lips, Juvederm Ultra plus. If just the line is bothering you, then I recommend only treating the line.  Consult with a board-certified plastic surgeon or dermatologist in your area to explore the best options for you. Good luck.

That line between your lower lip and chin is called the mental crease.  The top of the mentalis muscle inserts here and can aggravate the deepening of this line if you contract it a lot.  Neurotoxin can help with this.  Additionally hyaluronic acid filler such as juvederm, versa or restylane can injected to "pop" out the crease.  Sometimes this area needs more filler that it seems at first glance. 
If you want to add volume to the lower lip make sure there is support in the cutaneous lower lip and mental crease area.  Simply putting volume in the lip itself may cause a rolling effect and inadvertently make the mental crease look worse.
Hope this make sense!  Best of luck to you,
Dr. Amy