We consider a diffusion process $X$ in a random Lévy potential $V$. We study the rates of convergence when the diffusion is transient under the assumption that the Lévy process does not possess positive jumps. We generalize the previous results of Hu-Shi-Yor (1999) for drifted Brownian potentials. In particular, we prove a conjecture of Carmona: provided that there exists $0<\kappa<1$ such that $E[e^{\kappa V_1}]=1$, then $X_t/t^\kappa$ converges to some non-degenerate distribution. These results are in a way analogous to those obtained by Kesten-Kozlov-Spitzer (1975) for the random walk in a random environment.