'cleanly-operated' originates from English compound elements: 'cleanly' (derived from 'clean' + the adverbial suffix '-ly') and 'operate' (from Latin via later borrowings).

'clean' comes from Old English 'clǣne'; 'clean' formed the adverb 'cleanly' by adding '-ly'. 'Operate' derives ultimately from Latin 'operari' (to work), through Late Latin/Old French forms into Middle English 'operate'. These elements combined in modern English to form the descriptive compound 'cleanly-operated'.

Initially 'clean' meant 'free from dirt' and 'operate' meant 'to work or run'; combined as 'cleanly-operated' the phrase came to mean 'run or managed in a clean/hygienic way' in contemporary usage.