How long does it take for numbness in chin and lip to go away after oral surgery, removal of cyst on lower jaw bone?

Cyst. It all depends on the depth of the cyst and it's proximity to the nerve. As long as the nerve was not severed then it may take 4-6 months. If not then see a special oral surgeon who does nerve repair.
Type of injury. I am assuming injury is with the nerve of the lower jaw. If cyst is large & close to nerve, injury can occur. Less serious injury with the nerve still intact may take few weeks to a couple of months. If the nerve is physically injured it may take months. Evaluation with the dentist that did the surgery should be done now to obtain best resolution to your persistent numbness.
Nerve regrowth. If the coverings over a nerve, myelin, alone is affected, perhaps about 4 weeks, but if more extensive axonal involvement, regrowth at speed of fingernail lengthening, 0.1 mm daily.