Overcome being fed up with lunch (6)
I believe the answer is:
defeat
'overcome' is the definition.
(I know that overcome can be written as defeat)
'fed up with lunch' is the wordplay.
'up' says the letters should be written backwards (in down clue: letters go upwards).
'with' means one lot of letters go next to another.
'lunch' becomes 'eat' (to lunch can mean to eat lunch).
'fed' backwards is 'def'.
'def'+'eat'='DEFEAT'
'being' is the link.
(Other definitions for defeat that I've seen before include "Opposite of victory" , "Overwhelm" , "Vanquish, win against" , "failure" , "Loss" .)