What is the best way to cover/ bandage a lower lip after Mohs surgery? (photo)

For lower lip wounds like yours, I have my patients clean the wound twice daily with sterile normal saline to prevent buildup and solidifying of all yellowish exude. They are then directed to apply just Vaseline to the wound to keep it moist . Topical antibiotics should be avoided. A non-stick dressing such as Telfa  can be secured to the lower portion of the cutaneous lip with hypoallergenic paper tape such as Scanpore with the upper portion placed on top of the Vaseline. While this upper portion is not ideal and may have to be "re-stuck" frequently, it serves the purpose. While this may be annoying, the lower lip generally heals quickly. The non-stick dressing is not necessary but does add some extra protection when you are out and about. I am very surprised that you were not supplied with appropriate instructions.