Gas kinematics affect the radiative transfer and escape of hydrogen Lyman-α (Lyα) emission from galaxies. We investigate this interplay empirically by relating the ionised gas kinematics of 42 galaxies in the extended Lyα Reference Sample (eLARS) with their Lyα escape fractions, fescLyα, Lyα equivalent widths, EWLyα, and Lyα luminosities, LLyα. To this aim we use PMAS integral-field spectroscopic observations of the Balmer-α line. Our sample contains 18 rotating discs, 13 perturbed rotators, and 13 galaxies with more complex kinematics. The distributions of fescLyα, EWLyα, and LLyα do not differ significantly between these kinematical classes, but the largest Lyα observables are found amongst the kinematically complex systems. We find no trends between either fescLyα or EWLyα and kinematic or photometric inclinations. We calculate shearing velocities, υshear, and intrinsic velocity dispersions, σobs0 (empirically corrected for beam-smearing effects), as global kinematical measures for each galaxy. The sample is characterised by highly turbulent motions (30 km s−1 ≲ σobs0 ≲ 80 km s−1) and more than half of the sources show dispersion-dominated kinematics. We uncover clear trends between Lyα observables and global kinematical statistics: EWLyα and LLyα correlate with σobs0 , while fescLyα anti-correlates with υshear and υshear/σobs0 . Moreover, we find, that galaxies with EWLyα ≥ 20 Å are characterised by higher σ0 and lower υshear/σobs0 than galaxies below this threshold. We discuss the statistical importance of υshear, σobs0 , and υshear/σobs0 for regulating the Lyα observables in comparison to other galaxy parameters. It emerges that σobs0 is the dominating parameter for regulating EWLyα and that is as important as nebular extinction, gas covering fraction, and ionising photon production efficiency in regulating fescLyα. A simple scenario where the starburst age is simultaneously regulating turbulence, EWLyα, and fescesc is not supported by our observations. However, we show that the small-scale distribution of dust appears to be influenced by turbulence in some galaxies. In support of our observational result, we discuss how turbulence is theoretically expected to play a significant role in modulating fescLyα