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We study the present-day rotational velocity (Vrot) 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 $82{{\ \rm per\ cent}}$ of the galaxies have GCs that are rotating along the photometric major axis of the galaxy (aligned), while the remaining $18{{\ \rm per\ cent}}$ 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 ($49{{\ \rm per\ cent}}$), flat ($24{{\ \rm per\ cent}}$), and increasing ($27{{\ \rm per\ cent}}$) based on the Vrot/σ profiles out to large radii, we do not find any clear correlation between these present-day Vrot/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 $10\, \mathrm{Gyr}$ so that the ex-situ GCs are misaligned by an angle between 0° (co-rotation) and 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 (R200) from the centre of galaxies in 3D phase-space diagrams.