I’m a little late to this post but I do have Gonzalez Rivera ancestors from Lares.
My great grandfather was Manuel Gonzalez Rivera, born 1906 in Lares, Puerto Rico.
His parents were Gregorio Gonzalez and Maria del Pilar Rivera Caban (or Soto)
I do not have much on Gregorio, but he was about 35 years old when Manuel was born, which means he was born about 1870/1871. He is never listed with a second last name and he got the Gonzalez surname from his mother, Ramona Gonzalez.
My grandmother says that her grandfather migrated to Puerto Rico from Corsica, however I think it is more likely that her great grandfather rather than her grandfather, was the one that came from Corsica or even prior generations than that. Gregorio’s parents are listed as originally from Puerto Rico on the 1910 census.
Let me know if the above rings a bell. Thanks