This is a warning not to brag about what you expect to happen tomorrow. This can be stated clearly. AT: "Do not speak proudly about your plans for tomorrow" (See: [[rc://en/ta/man/translate/figs-explicit]])
Something happening on a certain day is spoken of as if the day were to bring that event. AT: "what will happen on a day" or "what will happen tomorrow" (See: [[rc://en/ta/man/translate/figs-metaphor]])
# your own mouth ... your own lips
Here a person is represented by his "mouth" and "lips" becuase those are the parts of the body used to speak. AT: "yourself ... yourself" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
The missing words can be supplied from the phrase before this. AT: "let a stranger praise you and not your own lips" (See: [[rc://en/ta/man/translate/figs-ellipsis]])