I think that Maurizio gave you a good answer. It's more probable that Giovanni Lorenzo is the grandfather's name (and in this case he was surely known as "Gianlorenzo") rather than Giovanni the gf and Lorenzo the ggf (in this second case it's highly probable that we had found a "filio" or a "quondam" between the two names). It's not impossible to find this form to indicate two different people (I did find it), but actually it's unusual (I also did ask to other genealogists to be sure: http://www.tuttogenealogia.it/index.php ... pic&t=3597 ). However, you'll find the final answer in your future researches.
L.
