Excitation functions for the production of heavy residues have been measured for the collisions 6, 7 Li+ 64 Zn at energies around and below the Coulomb barrier. The cross sections for heavy residue production have been measured using an activation technique, detecting off-line the characteristic atomic x-rays emitted in the electron capture decay of the reaction products. The experimental relative yields of the residues have been compared with statistical model calculations performed by using the code cascade. Such a comparison suggests that heavy residue production is dominated by complete fusion at above-barrier energies, whereas different processes like incomplete fusion and/or transfer become dominant in the sub-barrier energy region. The heavy residue excitation function ratio between the 6 Li-and 7 Li-induced collisions shows an increasing trend as the energy decreases below the barrier.