We propose a LSST Solar System near-Sun Survey, to be implemented during twilight hours, that extends the seasonal reach of LSST to its maximum as fresh sky is uncovered at about 50 square degrees per night (1500 sq. deg. per lunation) in the morning eastern sky, and surveyable sky is lost at the same rate to the western evening sky due to the Earths synodic motion. By establishing near-horizon fence post picket lines to the far west and far east we address Solar System science use cases (including Near Earth Objects, Interior Earth Objects, Potentially Hazardous Asteroids, Earth Trojans, near-Sun asteroids, sun-grazing comets, and dormant comets) as well as provide the first look and last look that LSST will have at the transient and variable objects within each survey field. This proposed near-Sun Survey will also maximize the overlap with the field of regard of the proposed NEOCam spacecraft that will be stationed at the Earths L1 Lagrange point and survey near quadrature with the Sun. This will allow LSST to incidently follow-up NEOCam targets and vice-versa (as well as targets from missions such as Euclid), and will roughly correspond to the Earths L4 and L5 regions.