Thanks for all the replies.
I will look over a 'Minsgyberna' map, and hope that the names of places are in Roman letters, and not Cyrillic. I have looked over Google Maps, for towns that begin with 'L' and are roughly within 150 km of Minsk, and which might be about the same length as 'Ligia' and came up with the following -
I'll consult more maps, and take another look at US documents for the other sons of the father Simon Lavine, and hopefully be able to narrow things down. The only thing I'm certain of right now is that this particular Lavine family came from the Minsk gubernia, probably from a town that begins with the letter 'L'.
As for all the other Levin, Lavine, Levy families in Trenton NJ - I am not particularly convinced that all these families are related, even the ones that took the name 'Lavine'. Simon Lavine is listed as 'Levy' on the 1900 US census, and that may be just as accurate as Lavine. I have no idea what the original family surname was before they came to the US. On the Belarus database on Jewishgen, I've found Levin, Levitan, Levinsky, Levko, Lev, Levi, and so on. Way too many variations of Levin, and way too common a name.