There is a clue on the naturalization form about where this person is from. He swears off allegiance to both Russia and the Republic of Poland. There was no independent Republic of Poland until after World War I. I think this naturalization form was from 1922, but it is hard to make the date out. If it is 1922, then the petitioner knew that where he lived prior to coming to the US was now within the borders of Interwar Poland. At that time, Lida was part of Poland, though now it is in Western Belarus. [The borders of modern Poland are not quite the same as those for Interwar Poland]
So possibly Lida is meant for the town name, though 'Lita' is also the Yiddish name for Lithuania. And prior to World War I, the town Lida was within the borders of the Vilna Gubernia, most of which is now within the borders of modern Lithuania.
When I've been confronted with these difficult-to-interpret town names, I've found it more useful to research every other US document I can find on a person, including census records, draft cards, and even obituaries. And even more useful was searching out documents on siblings, first cousins, uncles, even children of first cousins, especially for relatives who came to the US after 1910 or so. Their documents may be more clear about where the extended family was from.
Also, I would research the person 'Sorin' who your relative was going to when he arrived in the US. That would be a person he knew from the old country.
I also notice there are 2-3 sentences written in the left had margin of the naturalization form, though they are hard to read. Those might prove useful, too.
Lock/Lak/Lok and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus