Could lidocaine cause permanent nerve damage?

Unlikely: The needle form the injection can cause temporary or permanent damage, but that is not very common.

Unlikely: The anesthetic will wear off and normal sensation will return in a few hours. Sometimes the nerve can be nicked during administrating the Lidocaine however rare.

Rare but possible: Lidocaine is one type of local anesthetic or "numbing medicine". It is used for numbing skin, in nerve blocks, and in epidurals. It should not be directly injected into a large nerve because the nerve could be damaged. This is why ultrasound is often used to place nerve blocks, so that the local anesthetic is injected near, not in, the nerve.