I've been wondering about this too, there doesn't seem to be any real consensus among the soapers. Logically both lye and soap is reasonably water soluble so there shouldn't be any problem to completely wash everything away... But you never know.
I'd say there's plenty of consensus if you're talking about soapers who understand the chemistry vs. ones who are afraid of "chemicals."
An alkali such as NaOH or KOH is a powerful chemical but it is not a long-lasting toxin such as DDT or uranium. NaOH and KOH break down quickly in the environment to reasonably safe chemicals such as sodium carbonate (soda ash) and the like. Anything with NaOH or KOH residues is perfectly safe to be reused for food after a good rinse and wash.
I am more particular about not reusing containers that have held full strength fragrance oils or essential oils. And I avoid using items for food that cannot be completely cleaned of all soap residues (a stick blender for example).
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A clarification -- New soapers may not realize this, so I want to suggest that you be careful about using the word "lye" to mean NaOH. The word "lye" can be used for any
alkali solution that can be used to make soap. This includes NaOH, KOH, sodium carbonate, potassium carbonate, and even baking soda (sodium bicarbonate).
And the word "lye" doesn't technically include alkali in solid form -- it really refers to only a liquid solution.
If we all know the context, I think it's okay to use "lye" in an informal way, but be careful to use the proper name if there's any reason people might not understand what you're talking about from the general context of the conversation.
I've seen this confusion happening more often of late. I don't want to be the "lye police", but I do want to explain so folks can better understand how to communicate effectively.