How baths keeper is winning the lot! (8,3,4)

'how baths keeper is winning' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'the lot' is the wordplay.
I cannot quite see how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
'lot' could be 'c' and 'c' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?