The Radak expounds on the last pasuk, saying “that it was proper for each Kohen that their lips are guarding the knowledge of mitzvos and statutes, by enunciating them with their lips to the Jews, as it says in the Torah: ‘To show the Children of Israel all the statutes that Hashem your G-D spoke by the hand of Moshe,’ and it also says ‘Instruct the laws of Yaakov and Your Torah to Israel;’ therefore, Yisrael requests Torah from their mouth.” (Click here for Hebrew text.)
The Torah, being the guide book of all mankind, given as a gift specifically to the Jewish people from Hashem, gives us the means to live life to the fullest , and when the Jewish people are aware of this they thirst for the knowledge of the Torah. Therefore Hashem set up instructors to properly instruct us in how to abide by the Torah. It would seem that the most practical way of going about showing everyone how to do the right thing is to verbally teach them what to do. This seems obvious , but what does the Navi mean when it says “For a priest's lips shall guard knowledge,” which the Radak interprets to mean “that it was proper of each Kohen for his lips to guard the knowledge of mitzvos and statutes?” Why are lips needed to guard knowledge? How are they guarding it?
In the previous pasuk the Navi relates: , “True Torah was in his mouth,” referring to the Kohen, that Toras Emes, as the pasuk reads, should be in his mouth. But isn’t all Torah true? The Radak explains that just as Hashem’s Torah is in his (the kohen’s) mouth, meaning he teaches it to the public, so too it shall be in his heart, this is Toras Emes, a Torah of truth, meaning he should not be saying one thing but in his heart be thinking something else. Indeed, this fits perfectly into the next few words of the pasuk: “and injustice was not found on his lips.”
In order to guard the mitzvos from being lost they must be observed by the people. The only way to properly observe the mitzvos is to be taught them. However the only way they can be properly taught in a fashion that they will be well received and observed is if the one who is teaching them has his lips in sync with his heart. If they aren’t, then the message will not be delivered clearly and appropriately, which in turn would put the mitzvos in peril of not being observed, hence becoming lost.
This does not only apply to Kohanim but to all who teach Torah.