We present a hybrid-lattice Boltzmann (LB) algorithm for calculating the flow of glass-forming fluids that are governed by integral constitutive equations with pronounced nonlinear, non-Markovian dependence of the stresses on the flow history. The LB simulation for the macroscopic flow fields is combined with the mode-coupling theory (MCT) of the glass transition as a microscopic theory, in the framework of the integration-through transients formalism. Using the combined LB-MCT algorithm, pressure-driven planar channel flow is studied for a schematic MCT model neglecting spatial correlations in the microscopic dynamics. The cessation dynamics after removal of the driving pressure gradient shows strong signatures of oscillatory flow both in the macroscopic fields and the microscopic correlation functions.