Will sliding genioplasty cause lower lip numbness, will it be permanent?

Hello - of course, a photo is very helpful. However, in general, you would only have temporary numbness. I've done many many of these and not had anyone with permanent numbness. It can be done through the mouth or externally. Yes, permanent numbness is more likely if you already have nerve injury. But, temporary numbness before wouldn't necessarily be a big problem.
And, do you mean your chin is short meaning too far back? Or, too short top to bottom? Because, you may do better with a chin implant. The recovery is much quicker, and there are still implants with a genioplasty, but there are other advantages. We do both so I am comfortable discussing.

The genioplasty bone incision is 'under' the nerve to the lip and chin and there is much less risk to injury compared to the lower jaw advancement. The 'gums' below the front incisors however can become numb but that is more minor