  With a sample of 48,161 K giant stars selected from the LAMOST DR 2
catalogue, we construct torus models in a large volume extending, for the first
time, from the solar vicinity to a Galactocentric distance of $\sim 20$ kpc,
reaching the outskirts of the Galactic disc. We show that the kinematics of the
K giant stars match conventional models, e.g. as created by Binney in 2012, in
the Solar vicinity. However such two-disc models fail if they are extended to
the outer regions, even if an additional disc component is utilised. If we
loosen constraints in the Sun's vicinity, we find that an effective thick disc
model could explain the anti-centre of the MW. The LAMOST data imply that the
sizes of the Galactic discs are much larger, and that the outer disc is much
thicker, than previously thought, or alternatively that the outer structure is
not a conventional disc at all. However, the velocity dispersion $\sigma_{0z}$
of the kinematically thick disc in the best-fitting model is about 80 km
s$^{-1}$ and has a scale parameter $R_{\sigma}$ for an exponential distribution
function of $\sim 19$ kpc. Such a height $\sigma_{0z}$ is strongly rejected by
current measurements in the solar neighbourhood, and thus a model beyond
quasi-thermal, two or three thin or thick discs is required.
