This is education, not advice
The information here is written for the general reader and does not replace a personal medical consultation. It cannot tell you how much sensation in your own lip would return or whether an operation on your jaw is appropriate for your health or your circumstances.
A cut in bone is still an operation
A genioplasty is carried out under an anaesthetic, and the risks of bleeding under the soft tissue, infection around the plates, disturbed feeling in the lower lip and chin, damage to the tooth roots near the cut, and a result that is not the one intended apply. Nothing on this site should be read as saying that the operation is a small one.
No outcome is guaranteed
No treatment can be guaranteed. How much the soft tissue follows the segment, how the crease under the lip settles, and how much feeling returns vary between individuals, and the result is judged honestly at three months or later rather than in the first weeks.
Numbness and the second operation
Disturbed feeling in the lower lip and chin is expected after this operation and may remain reduced in part of the lip or chin for good. A second cut in the same bone carries a higher chance of that being lasting, and no surgeon can promise that sensation will return fully.