What do you think is “the lesson” Jekyll refers to in chapter 5? What text evidence helps to demonstrate his feelings about this “lesson”?

I'm unsure about the exact "lesson" you are referring to. Much of this chapter consists of a contrast between Utterson and Jekyll. Utterson is still quite the Victorian gentleman, putting image and appearance above all else. To protect Jekyll's reputation, he goes to visit him and discuss the issue personally rather than informing the police of Jekyll and Hyde's relationship and having them do the questioning. Moreover, even upon discovering Hyde's letter is almost certainly a forgery, Utterson refrains from confronting Jekyll. In this way, Utterson loyally protects his friend. In contrast, Jekyll lies to Utterson, defending Hyde with a fake letter. Here, for the first time, the reader begins to see hypocrisy in Dr. Jekyll. He claims to be a loyal and honest man, but in fact he is a liar and forger.