We present results for 19 Lyman Break Analogs (LBAs) observed with Keck/OSIRIS with an AO-assisted spatial resolution of less than 200 pc. We detect satellites/companions, diffuse emission and velocity shear, all with high signal-to-noise ratios. These galaxies present remarkably high velocity dispersion along the line of sight(- 70 km s-1), much higher than standard star-forming spirals in the low-redshift universe. We artificially redshift our data to z - 2.2 to allow for a direct comparison with observations of high-z LBGs and find striking similarities between both samples. This suggests that either similar physical processes are responsible for their observed properties, or, alternatively, that it is very difficult to distinguish between different mechanisms operating in the low versus high redshift starburst galaxies based on the available data. The comparison between morphologies in the UV/optical continuum and our kinemetry analysis often shows that neither is by itself sufficient to confirm or completely rule out the contribution from recent merger events. We find a correlation between the kinematic properties and stellar mass, in that more massive galaxies show stronger evidence for a disk-like structure. This suggests a co-evolutionary process between the stellar mass build-up and the formation of morphological and dynamical sub-structure within the galaxy.