It is relevant, on a pshat level, because he did not know Yosef. Had it just been a new king who did know Yosef, things might have been different. But since he didn't know Yosef, he acted in a certain manner towards the Jews, which was inappropriate based on their relationship to Yosef.
The commentators that provide alternative readings likely do so because it was inconceivable to them that this king didn't know Yosef, living so shortly after he had saved Egypt from a major famine and had been second in command in the country.
To solve this problem without diverting from the literal meaning of this phrase, Rav Hirsch (Shemot 1:8) suggests that the ruler was foreign, and therefore literally didn't know what had happened previously in Egypt.
(As for lessons, which the OP asked for: There are many lessons that can be learned from this, such as to make sure you are aware of all of the details in a story before acting in one way or another. Also, as Rav Hirsch notes there, the people of Egypt found themselves in a very complicated situation with a new hostile and foreign king, who was oppressing a nation that had been near and dear to the Egyptians in the years prior.)