One link online concerning Babylonian haruspicy (i.e. the practice of divining the future through sheep livers) may oddly enough help us shed some light on Etruscan rites, beliefs and cosmology: Sacrificial divination: Confirmation of extispicy. It shows a map of the sheep's liver and explains the significance to Babylonian ritual. There is also a very informative book called Babylonian Liver Omens where on page 45 a graphic shows the various parts of the liver as they were identified in the Babylonian language. This is followed by a lengthy explanation of the religious significance of each section.
Looking back at the Piacenza Liver, the middle section appears to me to have a direct connection to the Bāb Ekalli (aka. "The Palace Gate"). On page 46, it states:
"Symbolic value (OBE, 60): the palace, its internal affairs and the city gate and its incoming and outgoing traffic. In 62 Pān tākalti Tablet 5 many apodoses concern life and intrigue at the palace, only very few refer to the city gate."This then seems to connect back to the tripartite division of the inner section of the Piacenza Liver that I suggested previously in Solving the inner portions of the Piacenza Liver. This particular section would correspond to the earthly "middle world", pertaining to the world of humankind.