A lot produced by Charlie in Bath (5)
I believe the answer is:
batch
'a lot' is the definition.
('batch' can be a synonym of 'lot')
'charlie in bath' is the wordplay.
'charlie' becomes 'c' (phonetic alphabet: alpha, bravo, charlie etc.).
'in' indicates putting letters inside.
'c' inserted into 'bath' is 'BATCH'.
'produced by' acts as a link.
(Other definitions for batch that I've seen before include "Production run" , "Group of similar people" , "All the bread produced at one baking" , "Set, collection" , "Quantity of goods produced" .)