Woman did lie about duke (4)
I believe the answer is:
lady
'woman' is the definition.
(I know that lady is a type of woman)
'did lie about duke' is the wordplay.
'did lie' becomes 'lay' (past tense of 'lie').
'about' means one lot of letters goes inside another.
'duke' becomes 'd' (abbreviation).
'lay' placed around 'd' is 'LADY'.
(Other definitions for lady that I've seen before include "Lord's partner" , "Luck, for example" , "See 20" , "mature woman" , "older female" .)