Closure relations are presented for the lift coefficient for ordered arrays of 2-D and 3-D bubbles at various bubble volume fractions. These were determined via lattice Boltzmann simulations of bubble rise in periodic boxes, where the bubbles were also subjected to shear. The single-bubble lift coefficient, determined by low-shear computational experiments, varies in a systematic manner with the aspect ratio of the bubbles. At high shear rates the lift coefficient manifested a noticeable shear rate-dependence and it could even become negative. Through a linear stability analysis of the uniformly bubbling state, it is demonstrated that the lift force can destabilize a uniformly rising array of highly distorted bubbles and give way to columnar structures.