The original 3D Lorenz model is one of the most celebrated nonlinear dynamical system. A number of attempts have been made to generalize this model to higher dimensions and investigate high-dimensional chaos. In this paper, the 3D Lorenz system is extended to higher dimensions by selecting higher-order horizontal and vertical modes in doubled Fourier expansions of a stream function and temperature variations. The selection of the modes is guided by the requirements that they must conserve energy in the dissipationless limit and lead to systems that have only bounded solutions. The obtained results showed that the lowest-order Lorentz model that satisfies these criteria is a 8D system, and that the onset of chaos and routes to chaos in this high-dimensional system are different than that observed in the original Lorenz model. Physical explanation of these results is given.