Here a person is represented by his "mouth" and "lips" because those are the parts of the body used to speak. Alternate translation: "and do not let your own mouth praise you ... and do not let your own lips praise you" or "and do not praise yourself ... and do not praise yourself" (See: [[rc://en/ta/man/translate/figs-ellipsis]] and [[rc://en/ta/man/translate/figs-synecdoche]])
The words "let ... praise you" are understood from the first phrase. The words can be repeated here. Alternate translation: "let a stranger praise you" (See: [[rc://en/ta/man/translate/figs-ellipsis]])