What's the safest way to treat puncture wound of the lip?

Lip Puncture Wound. Get it evaluated in an er or urgent care. History and physical are required to assess for deep structure involvement, retention of foreign bodies, possible neurovascular damage, possible radiologic evaluation, updating tetanus status, etc. No other treatment may be required.
See physician. Important to see a doctor to evaluate the damage and wound. Initial cleaning, rinsing and irrigating with dilute peroxide (about 50% dilution), cover outside with antibiotic ointment and place damp wash cloth/ice to site. Then seek medical examination with your doctor or an urgent care facility. They will further clean, remove debris, and may give vaccination/antibiotic therapy.
Clean,tetanus. If you have not tetanus shot in 5 years see md. Otherwise clean wound and watch for sign of infection. Rhis will leave a s at which can be repaired by suturing initially or by laser later.