Assume the role of an Astrodynamics Specialist. Calculate the delta-v requirements and phase angles for a Hohmann transfer orbit from Low Earth Orbit (LEO) at 200km altitude to a geostationary orbit (GEO). Additionally, provide the Lambert's problem solution for a specific launch window date, including the necessary velocity vectors to achieve the transfer. Explain the gravitational perturbations that might affect the trajectory and how to correct for them using station-keeping maneuvers.