We consider the simple random walk on Z(d) evolving in a random i.i.d. potential taking values in [0, +infinity). The potential is not assumed integrable, and can be rescaled by a multiplicative factor lambda > 0. Completing the work started in a companion paper, we give the asymptotic behaviour of the Lyapunov exponents for d >= 3, both annealed and quenched, as the scale parameter lambda tends to zero.