I'm resurrecting this discussion, because I have finally figured out the ancestral town for my Lavine family, who settled in Trenton, New Jersey.
I contacted two different persons on Ancestry.com, who had my great great grandfather Simon Lavine in their trees. One of those individuals recently forwarded to me a written family history that was put together back in the 1990s, which did have enough information to show my great great grandfather was related to the larger Lavine clan of Trenton. It stated that he was one of four brothers, three of whom came to the US; the parents' names on Simon Lavine's NJ death certificate are in line with the parents' names of the other two Lavine brothers. The family history also stated that the ancestral town was Lida, and referenced two ship passenger lists, that I was able to find on Ancestry and verify that the town shown was Lida.
I also took another look at the 1920 US census, where Simon Lavine said he was from Minsk, presumably referring to the gubernia. In the same district, the same enumerator Mrs. Koplowitz also interviewed a daughter and a niece of Simon Lavine, and those two women said they were born in Vilna gubernia, which is more in line with Lida being the town.
Finally, combing through another tree on Ancestry that included my great great grandfather, and that had a lot of images attached to the tree, I found a nephew Isadore Lavine stating in his WW II draft card that he was born in Lida.
So that is the end of the mystery. Thanks to all for motivating me to look further into this subject.
I must note - this is one of the minority of times that public trees on Ancestry have been helpful to me, rather than being cornucopias of misinformation.
Lock/Lak/Lok and Kalon in Zagare/Joniskis/Gruzdziai, Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman/Lippman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lewin/Levin in Trenton, New Jersey and Lida/Vilna gub., Belarus