We report for the first time a relationship between galaxy kinematics and net Lyman-α equivalent width (net Lyα EW) in star forming galaxies during the epoch of peak cosmic star formation. Building on the previously reported broadband imaging segregation of Lyα-emitting and Lyα-absorbing Lyman-break galaxies (LBGs) at z ∼ 2 (Paper I in this series) and previously at z ∼ 3, we use the Lyα spectral type classification method to study the relationship between net Lyα EWand nebular emission-line kinematics in samples of z ∼ 2 and z ∼ 3 LBGs drawn from the literature, for which matching rest-frame UV photometry, consistently measured net Lyα EWs, and kinematic classifications from integral field unit spectroscopy are available. we show that z ∼ 2 and z ∼ 3 LBGs segregate in colour-magnitude space according to their kinematic properties and Lyman-α spectral type, and conclude that LBGs with Lyα dominant in absorption (aLBGs) are almost exclusively rotation-dominated (presumably disc-like) systems, and LBGs with Lyα dominant in emission (eLBGs) characteristically have dispersion-dominated kinematics. We quantify the relationship between the strength of rotational dynamic support (as measured using vobs/2σint and vrot/σ0) and net Lyα EWfor subsets of our kinematic sample where these data are available, and demonstrate the consistency of our result with other properties that scale with net Lyα EWand kinematics. Based on these findings, we suggest a method by which large samples of rotation- and dispersion-dominated galaxies might be selected using broadband imaging in as few as three filters and/or net Lyα EWalone. If confirmed with larger samples, application of this method will enable an understanding of galaxy kinematic behaviour over large scales in datasets from current and future large-area and all-sky photometric surveys that will select hundreds of millions of LBGs in redshift ranges from z ∼ 2 – 6 across many hundreds to thousands of Mpc. Finally, we speculate that the combination of our result linking net Lyα EW and nebular emission-line kinematics with the known large-scale clustering behaviour of Lyα-absorbing and Lyα-emitting LBGs is evocative of an emergent bimodality of early galaxies that is consistent with a nascent morphology-density relation at z ∼ 2 – 3.