A detailed statistical mechanical study has been carried out on a microscopic interaction model of lipid monolayers on the air-water interface. The model is Pink's ten-state model which accounts for the internal conformational states of the lipid acyl chains and their statistics and mutual interactions. Particular attention is paid to the chain-melting phase transition of saturated lecithin monolayers (e.g., DPPC) and the microscopic phenomena which accompany this phase transition. By means of computer-simulation techniques we have calculated the equilibrium and nonequilibrium isotherms and obtained quantitative measures of the lateral density fluctuations in the transition region in terms of the size distribution of lipid domains and the average coherence length of the conformational order of the acyl chains. Indications of the presence of a critical point are obtained. The results are compared with experimental observations of DPPC lipid monolayer phase behavior with special emphasis on an understanding of the origin of the nonhorizontal experimental isotherms.