'anti-lyrical' is formed from the prefix 'anti-' (from Greek 'anti-' meaning 'against') plus 'lyrical' (from 'lyric', ultimately from Greek 'lyrikos' meaning 'of the lyre' or 'lyric').

'lyrikos' in Greek passed into Latin and then Old French as 'lyrique'/'lyricus', entering English as 'lyric' and then 'lyrical'; the modern compound 'anti-lyrical' is created by adding the productive prefix 'anti-' to the adjective 'lyrical'.

Originally the elements signified 'against the lyre/lyric' in a literal sense; over time the compound came to mean simply 'against lyricism' or 'not lyrical', a usage that emphasizes non-poetic, restrained, or anti-melodic qualities.