Crossword Genius

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


I believe the answer is:

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.