Lady I take out? (5)

I believe the answer is:

lydia

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'lady' is the definition.
(woman's name)

'i take out?' is the wordplay.
'take' becomes 'lyda' (I can't justify this - if you can you should believe this answer much more).
'out?' is an insertion indicator.
'i' put within 'lyda' is 'LYDIA'.

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(Other definitions for lydia that I've seen before include "Girl's name - ancient kingdom in Asia Minor" , "Old kingdom" , "'Love for --' (H.E. Bates)" , "lady" , "girl" .)

I've seen this clue in The Globe and Mail.

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