The lady died in Slough (4)
I believe the answer is:
shed
'slough' is the definition.
(both can mean to remove or lose)
'the lady died' is the wordplay.
'the lady' becomes 'she' (I've seen this in other clues).
'died' becomes 'd'.
'she'+'d'='SHED'
'in' acts as a link.
(Other definitions for shed that I've seen before include "warehouse" , "Dump" , "In which lawnmower is kept" , "Outbuilding with a single story" , "Hut - throw off - Guardian cryptic crossword setter" .)