Shed tears over that Lady in Red? (6)
I believe the answer is:
cherry
'red?' is the definition.
(cherry is a kind of red)
'shed tears over that lady' is the wordplay.
'shed tears' becomes 'cry' (I've seen this before).
'over' indicates putting letters inside.
'that lady' becomes 'her' (I've seen this before**).
'cry' going around 'her' is 'CHERRY'.
'in' is the link.
(Other definitions for cherry that I've seen before include "Greyfriars Bob" , "Small succulent red stone-fruit" , "Deep red like small round fruit" , "Cricket ball" , "Small red stone-fruit from tree" .)