We present a three dimensional velocity analysis of Milky Way disc kinematics using LAMOST K giant stars and the GPS1 proper motion catalogue. We find that Galactic disc stars near the anticentre direction (in the range of Galactocentric distance between R = 8 and 13 kpc and vertical position between Z = -2 and 2 kpc) exhibit asymmetrical motions in the Galactocentric radial, azimuthal, and vertical components. Radial motions are not zero, thus departing from circularity in the orbits; they increase outwards within R ≲ 12 kpc, show some oscillation in the northern (0 < Z < 2 kpc) stars, and have north-south asymmetry in the region corresponding to a well-known nearby northern structure in the velocity field. There is a clear vertical gradient in azimuthal velocity, and also an asymmetry that shifts from a larger azimuthal velocity above the plane near the solar radius to faster rotation below the plane at radii of 11-12 kpc. Stars both above and below the plane at R ≳ 9 kpc exhibit net upward vertical motions. We discuss some possible mechanisms that might create the asymmetrical motions, such as external perturbations due to dwarf galaxy minor mergers or dark matter sub-haloes, warp dynamics, internal processes due to spiral arms or the Galactic bar, and (most likely) a combination of some or all of these components.