How do you remove rancid oder from lipstick?

You don't. Rancid smelling lipstick is usually due to to the product passing it's shelf life. It is best to dispose of lipstick after one to two years or if it starts smelling funky, as it may cause irritation. If one really wants to mask the odor, then perhaps essential oils may work, and chances are, the odor is conning from the entire product so it may be impossible to remove it.

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A thought...if your lipstick contains shea butter, it'll smell rancid because that's what shea butter smells like.