In this work, we study mixed layer lateral dispersion that is enhanced by near-inertial internal Poincaré waves in the offshore region of a large stratified lake, Lake Michigan. We examine the hypothesis that the vertical shear created by near-inertial internal Poincaré waves is not only an energy source for vertical mixing in the thermocline and mixed layer, but also enhances horizontal dispersion via an unsteady shear flow dispersion mechanism. Complex empirical orthogonal function analysis reveals that the dominant shear structure is observed to mirror the thermal structure, with the location of maximum shear gradually lowered as the mixed layer deepens. This changing structure of shear and vertical mixing produces different characteristics in shear flow dispersion between the early and later stratified periods. The estimated depth-averaged surface layer vertical turbulent diffusivity grows from 10^-5 m²s^-1 to 10^-3 m²s^-1 over the stratified period, and the associated lateral dispersion coefficients are estimated as 0.1 - 40 m²s^-1. The Poincaré waves are found to enhance greatly lateral dispersion for times less than the inertial period following release. In contrast, sub-inertial shear is the dominant mechanism responsible for shear dispersion for times greater than the inertial period. A simple approximation of the dispersion coefficient for lateral dispersion is developed, which scales as the product of surface current velocity (or wind friction velocity) and mixed layer depth. The calculated dispersion coefficients agree well with Okubo's diffusion diagram for times up to a week, which suggests that unsteady shear dispersion is a plausible mechanism to explain observed dispersion rates in the mixed layer for early times after release.