A new approximate integral equation with no empirical or adjustable parameters which was recently proposed [J. Chem. Phys. 110, 3961 (1999)] is used for the systematic study of Lennard-Jones fluid. The Ornstein-Zernike (OZ) equation designed originally to describe the thermodynamically stable states is substantiated to be valid also for predicting and studying the metastable states. Both stable and metastable solutions of the OZ equation are analyzed. The problem of determining the chemical potential is considered within the framework of the exact series of the bridge functionals. The structure and thermodynamic properties calculated from proposed approaches show excellent agreement with simulations for both stable and metastable states. Displayed and discussed is the gas-liquid phase diagram predicted by the new equation. Also, to build the liquid-crystal phase diagram some one-phase empirical structural criteria are utilized.