A new mesoscale two-phase flow non-dimensional lattice Boltzmann model (NDLBM) is developed for dynamical simulations of emergence and dispersion of self-sustained vortex and energy structures in microbial suspensions. Microbial fluids are treated as two-phase fluids with interaction forces between the biofluid phase and the base fluid phase, and the bioforces are based on transient local relative velocities. Microbial concentrations, sizes, shapes, densities, viscosities, surface tensions, active indexes, self repelling coefficients, and the nonlinear drag between the two phases are included in the present model. Base fluid properties and temperatures are also included. Both macroscopic and mesoscopic governing parameters are expressed with physical means for each coefficient. Compared to previous single-phase fluid mixture absolute velocity based models, the present two-phase fluid model based on the relative velocity shows faster convergence and more stable results. Parametric studies have been performed for intensities and group sizes of active flow structures in wide ranges of physical properties and governing parameters. Vorticity and energy structure patterns and scales are illustrated to show the underlying mechanism.