Breath exhaled from a lush, drunk after swallowing vermouth (7)

'vermouth' is the definition.
Both the answer and definition are singular nouns.
Perhaps you can see a link between them that I don't see?

'breath exhaled from a lush drunk after swallowing' is the wordplay.
I cannot quite understand how this works, but
'a' is found in the answer.
'drunk' could be 'lit' (I've seen this in other clues) and 'lit' is located in the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?