We present lattice Monte Carlo simulations of the growth of streptavidin islands at a biotinylated lipid layer. The model employed takes into account attractive anisotropic lateral interactions between streptavidin tetramers. With a minimal set of interactions, we reproduce the formation of rectangular islands experimentally observed at pH > or = 9.0. Specifically, we analyze two scenarios of the island growth. First, if streptavidin is rapidly adsorbed at t = 0 (stepwise coverage change without ongoing adsorption), the average linear island size is found to grow according to the Lifshitz-Slyozov law, R proportional to t(1/3). Second, if the island growth occurs in parallel with streptavidin adsorption limited by diffusion in the solution, the Lifshitz-Slyozov law is also applicable, but only at the late stage, when the streptavidin coverage is appreciable.