'electrolytically' originates from Modern English, specifically the adjective 'electrolytic', where the prefix 'electro-' meant 'electricity' and the element 'lytic' derives from Greek 'lysis' meaning 'loosening' or 'dissolution'.

'electrolytic' developed from 'electrolysis' (coined in the 19th century from Greek elements), and later the adverbial form 'electrolytically' was formed in English by adding the suffix '-ally' to produce the modern adverb.

Initially it referred specifically to processes involving electrolysis; over time it retained this technical sense and is still used to mean 'by means of electrolysis' or 'in an electrolytic manner'.