'ad-lib' originates from Latin, specifically the phrase 'ad libitum,' where 'ad' meant 'to' or 'toward' and 'libitum' meant 'pleasure' or 'desire'.

'ad-libitum' (Latin phrase) was adopted into English usage as the direction 'ad lib' (meaning roughly 'at one's pleasure' or 'as desired'), and later shortened/converted into the verb/adjective form 'ad-lib' and its past form 'ad-libbed'.

Initially it meant 'at one's pleasure' (a direction, especially in music), but over time it evolved into the modern sense of 'to improvise' or 'performed without preparation'.