We extend the concept of packing dimension profiles, due to Falconer and Howroyd ['Packing dimensions of projections and dimension profiles', Math. Proc. Cambridge Philos. Soc. 121 (1997) 269-286] and Howroyd ['Box and packing dimensions of projections and dimension profiles', Math. Proc. Cambridge Philos. Soc. 130 (2001) 135-160], and use our extension in order to determine the packing dimension of an arbitrary image of a general Lévy process.