Fat Injections in Lips, Is this Possible?

Fat transfer like you describe is possible and a great treatment for the face. It doesn't have a very good longetivity in the lips, though. Filler injection in the office is a better option for the lips.

Fat injections to the lips is definitely possible. The "take" of the fat is variable, so you may need more than one procedure, but if done carefully the risk of lumpiness is low and the results can be very long lasting.

If you are looking to have lip augmentation performed for a specific event (such as a wedding) I would suggest having a filler injection instead, because the results are more predictable, although not as long lasting. Good luck!