Results of a calculation valid to all orders in the nuclear-strength parameter Z\alpha are presented for the two-loop Lamb shift, notably for the two-loop self-energy correction, for the ground and first excited states of ions with the nuclear charge numbers Z=60-100. A detailed comparison of the all-order calculation with earlier investigations based on an expansion in the parameter Z\alpha is given. The calculation removes the largest theoretical uncertainty for the 2p_j-2s transition energies in heavy Li-like ions and is important for interpretation of experimental data.