Spatially extended halos of H i Lyα emission are now ubiquitously found around high-redshift star-forming galaxies. But our understanding of the nature and powering mechanisms of these halos is still hampered by the complex radiative transfer effects of the Lyα line and limited angular resolution. In this paper, we present resolved Multi Unit Spectroscopic Explorer (MUSE) observations of SGAS J122651.3+215220, a strongly lensed pair of L∗ galaxies at z = 2.92 embedded in a Lyα halo of L Lyα = (6.2 ± 1.3) × 1042 erg s-1. Globally, the system shows a line profile that is markedly asymmetric and redshifted, but its width and peak shift vary significantly across the halo. By fitting the spatially binned Lyα spectra with a collection of radiative transfer galactic wind models, we infer a mean outflow expansion velocity of ≈211 km s-1, with higher values preferentially found on both sides of the system's major axis. The velocity of the outflow is validated with the blueshift of low-ionization metal absorption lines in the spectra of the central galaxies. We also identify a faint (M 1500 ≈ -16.7) companion detected in both Lyα and the continuum, whose properties are in agreement with a predicted population of satellite galaxies that contribute to the extended Lyα emission. Finally, we briefly discuss the impact of the interaction between the central galaxies on the properties of the halo and the possibility of in situ fluorescent Lyα production.