Well, I never did this, but when explaining LDing to others (what I don´t try very often) there were some problems coming up:
Many people say they already know it (not the term “lucid” , but the thing).This is difficult, cause you can hardly tell wether they really know what you are talking about, or if they just think they know.
My advice: Emphasize that you have to really know that you are dreaming, and that you have to know about your waking life.
Don´t try to use the word “control” while explaning what lucid dreaming is, cause many people had non-lucid dreams in which they were in control
One to whom I talked didn´t want to believe me at first.After some talking, he thought that lucid dreaming existed, but that it was completely different from normal dream/sleep.He thought of it as something like using your imagination to create pictures in your head while half-awake.In his opinion the definition of “sleeping” is that you have lost your counciousness
If it is wise to speak in puplic?
Don´t ask me, I never tryed 
But I think in a psychology class this might be more tolerated.Anyway, depends on the auditory.
Traumgänger