Rivers and lakes are intrinsically connected waterbodies yet they are rarely used to hydrologically constrain one another with remote sensing. Here we begin to bridge the gap between river and lake hydrology with the introduction of the LakeFlow algorithm. LakeFlow uses river-lake mass conservation and observations from the Surface Water and Ocean Topography (SWOT) satellite to provide river discharge estimates of lake and reservoir inflows and outflows. We test LakeFlow performance at three lakes using a synthetic SWOT dataset containing the maximum measurement errors defined by the mission science requirements, and we include modeled lateral inflow and lake evaporation data to further constrain the mass balance. We find that LakeFlow produces promising discharge estimates (median Nash-Sutcliffe efficiency=0.88, relative bias=14%). LakeFlow can inform water resources management by providing global lake inflow and outflow estimates, highlighting a path for recognizing rivers and lakes as an interconnected system.