I have a Tyrion Lannister in play.

I use Hear Me Roar! and dupe Tyrion with another copy in my hand.

What happens when the delayed effect resolves?

a. The Dupe is discarded because that was the card put into play. Tyrion stays.

or

b.All Tyrion's are discarded because of "(cannot be saved)"

Or if both are incorrect, what would happen?

Text on "Hear Me Roar!":

" Action: Put a [Lannister] character into play from your hand. At the end of the phase, if that card is still in play, discard it from play (cannot be saved)."

So, the delayed effect on "Hear Me Roar!" can only discard the exact card that the event put into play. If you use it to dupe a unique Lannister character, the "card" that is still in play is the dupe - not the character the dupe was put on. Only the dupe would be discarded at the end of the phase.

Note that if the effect said, "At the end of the phase, of that character is still in play,..." you wouldn't discard anything -- because the "character" put into play by the event isn't actually in-play (because it transformed into a dupe, and so is not a "character" anymore).

The most important thing to realize is that "if that card is still in play" will only ever refer to the exact piece of cardboard that was put into play. It will never refer to other cards or game elements, no matter what characteristics they share (title, duplicate "host", etc.) with the card put into play by the event.