Lidocaine1 is not categorized as a painkiller but as a (local) anesthetic; it can be used during minor procedures where the patient has full awareness by injecting it to the preferred site of action.
It inhibits the sodium channels on the nerve endings in the skin. Therefore it provides insensibility of ALL nerve fibers, both causing numbness in the skin and inhibiting the pain signals coming from that part of the skin.
The analgesics/painkillers listed above have are not categorized as anesthetics and they have a more central effect.
They are solely used for inhibiting pain but not for numbing. For example:
Paracetamol (acetaminophen)2 by example works by inhibiting the prostaglandine synthesis in the entire system. Prostaglandine is usually excreted by the site of action due to inflammation and when it is picked up by nerve fibers, one generally experiences pain.
Diazepam3 is neither of the above. It is an anxyiolytic benziodiazepine that is used when patients are in high levels of stress or anxiety before or after the procedure.
Peroral administration of analgesics is often advised by physicians before or after a minor procedure in case the patient is in pain or a lot of pain is expected by the physician.
In conclusion, lidocaine is not(painful-)painkilling but an anesthetic so it has to be used to obtain numbness of the skin in very painful medical procedures. Painless-painkilling (eg. ibuprofen, paracetamol) CAN be added afterwards or during the procedure but it is very uncommon to use this as only farmacological substance for such procedures as it does not provide insensibility and the patient can still feel everything and experience pain directly from the skinfibers.