Numbness of upper and lower lips is not likely associated with dental procedures and periapical infection. Assuming one side of lips is involved, it's more related to nerve dysfunction. Seeing a neurologist is advised.
Is the same dentist doing all this work himself? I would expect at least 2 specialists involved in the procedures you mentioned.
As for nerve damaged, where the nerve for the upper and lower lip connect is well beyond the scope of what the dentist can reach, so its unlikely to be caused by the implant.
If you don't understand your treatment, I would always suggest getting a second opinion.