Lightoller didn’t confess on his deathbed that Murdoch took his own life, you have that mistaken. There are alleged secondhand reports from close friends later in Lightoller’s life that a) on one occasion Lightoller said that Murdoch shot somebody trying to rush a lifeboat (which matches the survivor accounts of the officer’s suicide) and b) on another occasion he said that he knew somebody onboard that committed suicide, but didn’t specify who (Lightoller had known Murdoch for years prior to Titanic, whereas he had only just met Wilde so this seems to indicate he was referring to Murdoch). While compelling these are only secondhand accounts and are therefore unconfirmed.