So, it is my understanding in the context of Theseus that a "layer" is a hen that sits on her eggs, a sitter, a broody hen etc. which in Greek is κλώσσα (κότα).Which incidentally is also a derogatory term for someone who takes too long to do some work (πολύ το κλωσσάει το ζήτημα= he is taking too long to act on the issue). Now... I have no idea if there is a name for hens who are too old, other than to call them old (η γριά κότα έχει το ζουμί), so I have no idea how one would translate what you are asking. As for humans, the reproductive ability of a person is not an issue that is discussed in polite company and I don't know any Greek slang that specifically relates to the menopause.
In fact, I see the issue discussed a lot more in the UK than in Greece, and I don't mean on BBC radio, where I am sure they did a good job, but in what I called earlier "polite company". For some reason, English speakers appear to me concerned about it and about other functions of the reproductive system of women (and men to an extent), which are quite often described in very negative terms (the curse, the change etc.).
This indicates to an outsider that the main value of a woman is in her reproductive capacity and there is no value in an old woman who cannot bear children or do the housework, there appears to be little appreciation of the wisdom of old age etc. Yes, I appreciate that this is probably not the case after a century of women's rights campaigns, but it is perhaps an indication of the culture of the past.