We introduce an extended application of the off-lattice self-consistent-field theory (SCFT) to model lipid monolayers at air-water interfaces. The off-lattice SCFT is used without a priori symmetry assumptions on equilibrium morphologies. This enables us to capture asymmetric lipid membranes at air-water interfaces which are otherwise unattainable with a conventional SCF model. Equilibrium morphologies in systems containing lipid molecules, fractions of air, and water are studied as a function of the relative amount of lipid molecules. The corresponding Langmuir isotherms are analyzed to reveal possible phase transitions. We consider both saturated and unsaturated lipid molecules with a branched structure. For saturated lipids, we find two distinct phases, i.e., micellar and lamellar, showing a pronounced first-order phase transition with a well-defined region of phase coexistence. This region is sensitive to the hydrophilicity of lipid molecules and the miscibility of air with water molecules. The phase coexistence is also influenced by the size of hydrophilic and hydrophobic parts of lipid molecules. In contrast, membranes of unsaturated lipids have developed a continuous range of smooth structural transformations from a circular to an ellipsoidal micellar morphology and eventually to a lamellar structure. The shape of the lamella changes from a slightly undulated to a vigorously curved. Unlike saturated lipid membranes, there is no apparent first-order phase transition or a region of phase coexistence for unsaturated lipid membranes. We interpret this as a result of a higher flexibility of unsaturated lipid membranes which enables them to adopt a wider range of conformations in comparison with saturated lipid membranes.