  Context: The high quality of the Gaia mission data is allowing to study the
internal kinematics of the Large Magellanic Cloud (LMC) in unprecedented
detail, providing insights on the non-axisymmetric structure of its disc. Aims:
To define and validate an improved selection strategy to distinguish the LMC
stars from the Milky Way foreground. To check the possible biases that assumed
parameters or sample contamination from the Milky Way can introduce in the
analysis of the internal kinematics of the LMC using Gaia data. Methods: Our
selection is based on a supervised Neural Network classifier using as much as
of the Gaia DR3 data as possible. We select three samples of candidate LMC
stars with different degrees of completeness and purity; we validate them using
different test samples and we compare them with the Gaia Collaboration paper
sample. We analyse the resulting velocity profiles and maps, and we check how
these results change when using also the line-of-sight velocities, available
for a subset of stars. Results: The contamination in the samples from Milky Way
stars affects basically the results for the outskirts of the LMC, and the
absence of line-of-sight velocities does not bias the results for the
kinematics in the inner disc. For the first time, we perform a kinematic
analysis of the LMC using samples with the full three dimensional velocity
information from Gaia DR3. Conclusions: The dynamics in the inner disc is
mainly bar dominated; the kinematics on the spiral arm over-density seem to be
dominated by an inward motion and a rotation faster than that of the disc in
the piece of the arm attached to the bar; contamination of MW stars seem to
dominate the outer parts of the disc and mainly affects old evolutionary
phases; uncertainties in the assumed disc morphological parameters and
line-of-sight velocity of the LMC can in some cases have significant effects.
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