'antilethargic' originates from English combining the prefix 'anti-' (ultimately from Greek 'anti') meaning 'against' and the adjective 'lethargic' (from Greek 'lēthargikos'/'lēthargia') where 'lēthargia' meant 'forgetfulness, drowsiness'.

'lethargic' changed from Greek 'lēthargos' / 'lēthargia' to Late Latin 'lethargicus', passed into Middle English as 'lethargic' and eventually became the modern English adjective 'lethargic'. The prefix 'anti-' comes from Greek 'anti-' and has been used in English as a productive prefix meaning 'against' since Classical and Medieval borrowings.

Initially the elements meant 'against' (anti-) and 'drowsiness' or 'forgetfulness' (lethargic); combined, the formation came to mean 'against drowsiness' or 'counteracting lethargy', a sense retained in modern usage.