Lorenzo Spingola I don't think was related to the Taylor St Spingolas. From my Info, he entered the US around 1905 and settled in the Near North Little Sicily area, occupation later listed as baker. I'm not 100% certain but I believe he was Sicilian from Bagheria.
About the other Spingolas. They had several people tied into to Johnny Powers's political machine and its Italian successors in the 19th and 17th wards. Father Giuseppe Spingola was a precinct captain for "De Pow", as was son Peter Spingola. Henry of course ran for state senate but I'm not sure if he won that race (doesn't seem like it). Henry and Peter Spingola were both said to have been involved in the Genna faction. The brothers ran an auto garage which was used as an HQ by the Genna's, Amatuna, Tropea. Albert Anselmi was also spotted at the garage. Interestingly, shortly after Henry Spingola was clipped in January 1926, Agostino and Antonino Morici (the Westside Moricis) were killed. The papers of course reported that this was linked to the Spingola murder (in the sense that they thought these were all "Black Hand" extortion hits), but they also noted that the Moricis had recently purchased a Westside property from James Genna. So while the Genna faction seems to have largely been of Trapanese origin, these Morici may have been linked to it and I belive were from Bagheria. Something else to note.