The first man is taken in by me to see a lady (6)
I believe the answer is:
madame
'lady' is the definition.
(I know that madame is a type of lady)
'the first man is taken in by me' is the wordplay.
'the first man' becomes 'adam' (first man in the Bible).
'is taken in by' indicates putting letters inside.
'adam' going within 'me' is 'MADAME'.
'to see a' is the link.
(Other definitions for madame that I've seen before include "Book by Flaubert" , "Married woman abroad" , "French Mrs" , "Flaubert novel" , "French married woman" .)