The equilibrium nature and phase behavior of lipid monolayers and their applications (lipid rafts, lung surfactants, etc.) has been a long-standing topic of experimental and theoretical research for decades. Even so, studies that independently measure the line tension apart from the dipole density difference in solid-liquid monolayers are lacking. We address this deficit by applying Mullins-Sekerka theory in two-dimensions to model lung surfactant solid-liquid crystal interfaces. We observe a strong alignment between theory and experimental observations including a dominant growth frequency and various kinetic parameters and their impact on crystal morphology that are consistent with the Mullins-Sekerka perturbation theory. We suggest values for independently derived line tension and dipole density of solid lipid domains in a liquid phase melt.