This is an interesting one.
Delirium and delirious are the surviving children (along with a few other forms) of the obsolete verb delire, to be deranged, crazy, out of one’s wits. Originally, as OED goes on to say (and this is the part I found interesting), it meant to go out of the furrow, to deviate from the straight, its root being the Latin lira, ‘ridge, furrow, in ploughing’.
One forms the picture of a badly hung-over Roman slave blearily zig-zagging the oxen across the field until his enraged owner spots him. “Corvulo, you have delired on this farm for the last time. Your duties in future will centre around the cess-pit.”
Earliest cite in OED for delirium and delirious both is 1599.
The term delirium tremens, associated with alcohol, was introduced by Dr Sutton in 1813, although it then had a different meaning.
‘The term was introduced by Dr. Sutton, in 1813, for that form of delirium which is rendered worse by bleeding, but improved by opium. By Rayer and subsequent writers it has been almost exclusively applied to delirium resulting from the abuse of alcohol.’