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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, $ {f^\mathrm{Ly\alpha}_\mathrm{esc}} $ , Lyα equivalent widths, EW_Lyα, and Lyα luminosities, L_Lyα. 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 $ {f^\mathrm{Ly\alpha}_\mathrm{esc}} $ , EW_Lyα, and L_Lyα 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 $ {f^\mathrm{Ly\alpha}_\mathrm{esc}} $ or EW_Lyα and kinematic or photometric inclinations. We calculate shearing velocities, v_shear, and intrinsic velocity dispersions, $ \sigma_0^\mathrm{obs} $ (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 ≲ σ₀^obs ≲ 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: EW_Lyα and L_Lyα correlate with $ \sigma_0^\mathrm{obs} $ , while $ {f^\mathrm{Ly\alpha}_\mathrm{esc}} $ anti-correlates with v_shear and v_shear/σ₀^obs. Moreover, we find, that galaxies with EW_Lyα ≥ 20 Å are characterised by higher σ₀ and lower v_shear/σ₀^obs than galaxies below this threshold. We discuss the statistical importance of v_shear, $ \sigma_0^\mathrm{obs} $ , and v_shear/σ₀^obs for regulating the Lyα observables in comparison to other galaxy parameters. It emerges that $ \sigma_0^\mathrm{obs} $ is the dominating parameter for regulating EW_Lyα and that is as important as nebular extinction, gas covering fraction, and ionising photon production efficiency in regulating $ {f^\mathrm{Ly\alpha}_\mathrm{esc}} $ . A simple scenario where the starburst age is simultaneously regulating turbulence, EW_Lyα, and f_esc^esc 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 $ {f^\mathrm{Ly\alpha}_\mathrm{esc}} $ .