If I have the lannister iron throne in play that can cancel character triggered abilities, can I use it to stop my opponent from discarding a duplicate character to save a character from valar morghalis

Yes. The character gains the save Response from the duplicate. Because they gain that Response it's a character ability and can be canceled by Iron Throne.

Yes. The character gains the save Response from the duplicate. Because they gain that Response it's a character ability and can be canceled by Iron Throne.

As i understand it, duplicates are not character abilities, because they are not printed abilities on characters. They are a gained ability and therefore subject to things that cancel responses or triggered abilities, but not cancellation of character abilities.

Any ability that a character has is a character ability. Doesn't matter if it is gained gained or printed. Look at section 3.7 in the FAQ.

This is why some people are frustrated with some of MDC's posts and topics. Because they can lead to misinformation and confusion to even the more experienced players. I think stormwolf27 is recalling some stuff that MDC posted in that "3.7 vs 4.3" post that argued the gained save response from duplicates isn't a character ability. His argument wasn't the case.

possibly. I do have trouble sometimes recalling who said what in those long-winded threads. Plus, I don't always feel like reading a novel every time I want to try and answer a question, though, in hindsight, it might be a better idea from now on.

Dupe saves aren't a "printed character ability" but they are a "character ability".