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We study the present-day rotational velocity ($V_{rot}$) and velocity dispersion ($σ$) 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 $V_{rot}/σ$ profiles out to large radii, we do not find any clear correlation between these present-day $V_{rot}/σ$ 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° (co-rotation) to 180° (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.