  We present an analysis of observations with the Atacama Large
(sub-)Millimetre Array (ALMA) of the 380 GHz water emission line and CO (11-10)
emission line from MG J0414+0534, a gravitationally lensed dusty star-forming
galaxy that hosts a type 1 quasar. We also present observations at 1.6 GHz with
global very long baseline interferometry (VLBI) of the radio source. We confirm
the previously reported detection of the 380 GHz water line and that the flux
density ratio between the two merging lensed images is reversed with respect to
the radio/mm continuum. We further find tentative evidence of variability in
the integrated line intensity on timescales of days. We show that the 380 GHz
water line has two components of emission: a disc that is around 35 pc in
diameter around the quasar, and another component of emission that is offset
$\sim$600 pc perpendicular to the disc that lies close to the lensing caustic.
With lens modelling of the multi-wavelength data sets, we construct a model for
the quasar system consisting of a circumnuclear disc of molecular gas with a
size of about 60 pc bisected by radio jets extending to a distance of about 200
pc from the radio core. Our findings suggest that observations with ALMA of
high-excitation molecular lines from strongly lensed quasars could allow
detailed studies of AGN accretion and feedback at the cosmic peak of black hole
and galaxy growth.
