Crossword Genius

Drink beer on me, possibly after end of poll (6,5)

Ross

I believe the answer is:

bitter lemon

I'm a little stuck... Click here to teach me more about this clue!

'after end of poll' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'drink beer on me' is the wordplay.
'drink' becomes 'bitter' (bitter is a kind of drink).
'beer on me' becomes 'lemon' (I can't explain this - if you can you should believe this answer much more).
'bitter'+'lemon'='BITTER LEMON'

'possibly' is the link.

Can you help me to learn more?

(Other definitions for bitter lemon that I've seen before include "Soft citrus drink" , "Tart soft drink" .)

I've seen this clue in The Times.
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