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The salamander wouldn’t tell me the password, even though I talked to it with the Red Prince that has pet pal...
To clarify. The point isn't to have A lizard to talk to Xiuh (red salamander at Ryker's mansion). It's to have THE Red Lizard. A royalty. It working with Fane mask was a "bug" and "fixed" on Definitive Edition. To be able to talk to the fancy salamander and it share its secret, it need to acknowledge you as a majesty. If you don't have Red Prince in your group, you can either 1) eat the disembodied lizard leg from Stranger in a Strange Land or 2) get your way into Ryker's basement by accepting his quest to retrieve a tablet from Blackpits (after this and after leaving and coming back, the basement hatch will be uncovered and a servant will give you a note telling Ryker is waiting for you down there). At the north part of the basement, among other body parts, there'll be a disembodied leg that will teach you the song. The female lizard spirit near the chest tells you "an elf" didn't left empty handed. Luckly "an elf" left a leg...
For some reason, the song option didn't show up for me with the mask's lizard form, only the elf form that ate the leg
Learning the secret from a leg didn't give xp. Opening the chest this way gave the same amount of xp as the persuasion check
3) Have high persuasion (I did it with 4 points) and use Fane’s mask to turn into a lizard then talk to the chest and convince it to open for you. Best and easiest option if you’re lone wolf with no Red Prince. If you’re persuasion isn’t high enough just respec on the ship first and put it back into whatever (probably thievery) when done.
What you can do is have ANY lizard with a scholar tag talk to the salamander in rykers cheers!
Easy approach: Teleport the chest out of the flame, have the lizard prince talk to it (4 persuasions needed), and tell the chest that you have the authority to open the chest (because you are the prince). It'll open for you and you loot the chest. No other quests needed.