Jamieson, Fausset and Brown on Leviticus 13:45

45. the leper in whom the plague is, his clothes shall be rent, &c.--The person who was declared affected with the leprosy forthwith exhibited all the tokens of suffering from a heavy calamity. Rending garments and uncovering the head were common signs of mourning. As to "the putting a covering upon the upper lip," that means either wearing a moustache, as the Hebrews used to shave the upper lip [Calmet], or simply keeping a hand over it. All these external marks of grief were intended to proclaim, in addition to his own exclamation "Unclean!" that the person was a leper, whose company every one must shun.