Yeah having extra lives is pretty key. You should make sure you have at least 200 gold after each boss to buy another death defiance at the shop fountain if it's being offered. Also I think it's either Athena or Aphrodite that has some boons that will replenish death defiance.
I think the extra lives are more beneficial than the one death per chamber since you gotta figure most deaths probably come from bosses, especially the last one. Having at least one or two extra lives for the final boss is pretty huge.
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