The Lyman &agr; (Ly &agr;) sky background arises from the scattering of solar Ly &agr; from a spatial distribution of neutral hydrogen in interplanetary space. This distribution is partially determined by the solar wind proton flux, which provides the principal mechanism of loss by charge exchange of the neutral hydrogen. By generating isophotal maps of scattered Ly &agr; for several choices of interstellar wind direction and solar wind proton flux distributions, the results show that latitudinal variations of the solar wind proton flux can have a significant effect on the observed location and shape of the Ly &agr; intensity maximum. This fact should aid in the interpretation of Ly &agr; maps and also indicates a possible method for inferring values for the average solar wind proton flux out of the ecliptic plane.