Vertical structure and kinematics of the LMC disc from SDSS/Gaia

[Abbreviated] Context: Studies of the LMC's internal kinematics have provided a detailed view of its structure, largely by the exquisite proper motion data supplied by Gaia. However, LoS velocities are only available for a small subset of Gaia data, limiting studies of the kinematics perpendicular to the LMC disc plane. Aims: We synergise new SDSS-IV/V LoS velocity measurements with Gaia data, increasing the 5D phase-space sample by almost a factor of three. We interpret and model the vertical structure and kinematics of the LMC disc. Methods: Split our sample into different stellar types. Then examine maps of vertical velocity moments perpendicular to the LMC disc. We interpret our results within three possible scenarios: 1) time-variability in the orientation of the disc symmetry axis; 2) use of an incorrect LMC disc plane orientation; or 3) the presence of warps or twists in the LMC disc. We also present a new method to construct a continuous 3D representation of the disc from spatially-resolved measurements of its viewing angles. Results: Using young stellar populations, we identify a region in the LMC arm with highly negative v_z'; this overlaps spatially with the supershell LMC 4. Our results indicate that: 1) the LMC viewing angles may vary with time, but this cannot explain most of the structure in v_z' maps; 2) when re-deriving the LMC disc plane by minimising the RMS vertical velocity v_z' across the disc, the inclination and line-of-nodes position angle are i ~ 24 degr and \Omega ~ 327 degr, respectively; 3) we obtain different inclinations for the inner and outer disc regions, and a quadrupolar variation with azimuth in outer the disc. We provide 3D models of the LMC disc shape. Conclusions: The combination of SDSS-IV/V and Gaia data reveal that the LMC disc is not a flat plane in equilibrium, but that the central bar region is tilted relative to a warped outer disc.