Are there alternative therapies for puncture wound of the lip?

Depends. Most puncture wounds to the lip will generally heal on their own unless there is a significant tear or laceration that requires suturing. The only "alternative" to suturing is allowing healing to take place similar to a scab if one were to fall and scrape one's knee. It is important to make sure that tetanus is up to date and to look out for signs of infection: redness, swelling and/or pain.
Only If minimal. Alternative therapies may be reasonable in the face of minor trauma.
No. A puncture wound of the lip needs to be cleansed thoroughly. Some sort of antibacterial whether it be mouthwash, betadine, or simple soap and water is important. The blood supply of the lip is extraordinary and infection is very infrequently seen. Cosmetic wounds that involve the lip should be considered for suture closure.