Got it today (SOTFS 25/04/2022) on the 24th attempt. I saw 5 Red Lion Warrior Capes and numerous other pieces before having the helm drop. If you're trying to do this farm now I highly recommend putting steam into offline mode first because if you're online while the servers are off you will be forced to wait 30 seconds every time the game opens.
I was using Traveling Merchant Hat + Prisoner's Tatters + Watchdragon Parma + Covetous Gold Serpent Ring +2 + Rusted Coin (i'm before where you get the Jester hat on this character, I'm assuming that has better discovery than the Traveling Merchant Hat) and even then I was still sometimes getting no drop at all. Best farming strategy I've found was to just go up to the ruin area, clear out the other lions one by one and just save+quit there, then copy that save and put it somewhere. Open your DS2 saves directory where the current save is and after every attempt just Alt+F4, open the taskmanager and close the game's process in there (it won't close very quickly after an Alt+F4 on its own), replace the save in the directory with the one you backed up, boot the game back up, click through the popups to Continue, pop the Rusted Coin and do this over and over until RNG blesses you with whatever piece you fancy (the helm and red cape are the only things the Gold Lion Warrior drops that the others don't). Since the Gold Lion can only drop one item at a time if you want both of its unique pieces you will have to have at least 1 Bonfire Ascetic (2 if you killed him on NG before realizing he has actually has unique drops).
Good luck all.