  We study the present-day rotational velocity ($V_{rot}$) and velocity
dispersion (${\sigma}$) profiles of the globular cluster (GC) systems in a
sample of 50 lenticular (S0) galaxies from the E-MOSAICS galaxy formation
simulations. We find that 82% of the galaxies have GCs that are rotating along
the photometric major axis of the galaxy ($aligned$), while the remaining 18%
of the galaxies do not ($misaligned$). This is generally consistent with the
observations from the SLUGGS survey. For the $aligned$ galaxies, classified as
$peaked$ $and$ $outwardly$ $decreasing$ (49%), $flat$ (24%) and $increasing$
(27%) based on the $V_{rot}/{\sigma}$ profiles out to large radii, we do not
find any clear correlation between these present-day $V_{rot}/{\sigma}$
profiles of the GCs and the past merger histories of the S0 galaxies, unlike in
previous simulations of galaxy stars. For just over half of the $misaligned$
galaxies, we find that the GC misalignment is the result of a major merger
within the last 10 Gyr so that the $ex$-$situ$ GCs are misaligned by an angle
between 0{\deg} (co-rotation) to 180{\deg} (counter-rotation) with respect to
the $in$-$situ$ GCs, depending on the orbital configuration of the merging
galaxies. For the remaining $misaligned$ galaxies, we suggest that the
$in$-$situ$ metal-poor GCs, formed at early times, have undergone more frequent
kinematic perturbations than the $in$-$situ$ metal-rich GCs. We also find that
the GCs accreted early and the $in$-$situ$ GCs are predominantly located within
0.2 virial radii ($R_{200}$) from the centre of galaxies in 3D phase-space
diagrams.
