The lady had a backyard building (4)
I believe the answer is:
shed
'a backyard building' is the definition.
'shed' can be an answer for 'building' (shed is a kind of building). I'm not sure about the 'a backyard' bit.
'the lady had' is the wordplay.
'the lady' becomes 'she' ('she' refers to a woman).
'had' becomes 'd' (I've seen this in other clues).
'she'+'d'='SHED'
Can you help me to learn more?
(Other definitions for shed that I've seen before include "Basic building" , "Get rid of - hut" , "Outhouse -- cast" , "One-storeyed outbuilding" , "lost" .)