In a previous paper, 2D Jackson-Hunt (JH) analysis was extended by accounting for the curvatures of the transformation front for the case of binary systems with stoichiometric phase diagrams. In this study, it is generalized to any given phase diagram. That the steady state solute distribution satisfies zeroth order hypothesis is rigorously established in the present analysis as opposed to the previous theory's mere self-consistency proof. While the errors incurred due to low peclet number approximation, once the zeroth order approximation is implemented, were analyzed in the earlier work, the combined errors are estimated in the current article. The solute distribution of the current formulation is shown to be correct up to first order in peclet number as is the relative error in steady state velocity dependence on lamellar spacing and undercooling. For the practical cases of growths under an imposed temperature gradient, the formulation can be readily generalized to rapid solidification situations by recoursing to numerical algorithms for the estimation of solid phase fractions.