Two new cubic equations of state (EOS's) for the pure Lennard-Jones (LJ) monomer fluid are constructed using molecular simulation data for compressibility factor Z versus packing fraction eta isotherms. Simulation data for the LJ monomer and dimer pair correlation function at contact value derivatives are fit to extended (quartic) forms of these EOS's and used within the framework of Wertheim's first-order thermodynamic perturbation theory (TPTI) for both the monomer and dimer reference fluid to obtain ten new quartic in molar volume EOS's for straight, cyclic and branched LJ chain fluid isotherms. Predicted Z vs. eta for the new equations is compared to simulation data and predictions from much more complex published models. Results show that these simpler equations are much easier to use, with minimal loss in accuracy. Finally, the LJ framework for individual cyclic chains is used in the Marshall-Chapman methodology for branched chains to derive two new LJ TPTI-D platforms and four new equations of state for "branched and fused rings". The models presented in this paper serve as a foundation for the development of molecularly-based EOS's for real fluids with "soft" intermolecular and intramolecular potentials. (C) 2015 Elsevier B.V. All rights reserved.