Understanding the morphology of transformation of a single bubble immersed in a liquid undergoing a shear flow is essential in predicting bubble deformation and breakup phenomena commonly found in applications involving complex liquid-gas multiphase flow. In this study, the deformation and breakup of a single bubble released in a fully developed laminar Couette flow in a micro-scale domain are evaluated under different spanwise positions, as well as under different initial diameters. The simulation is carried out using a multiphase Shan-Chen Lattice Boltzmann Model (SC-LBM). The transition between deformation and breakup experienced by the bubble is described under different Capillary (Ca) numbers, viscosity ratios and relative initial spanwise positions with respect to the channel centreline. A critical Ca number, Cac = 0.31, was found at the onset of breakup, with bubble centroid location varying as a function of the remaining parameters. The results obtained with the SC-LBM are in excellent agreement with those published in the literature.