Interwar Lithuania did not require residents to get a external passport in order to leave the country. It was the Russian empire that required such a document.
And up until 1924, the US did not require immigrants to have a passport or visa to enter the country. After 1924, when the immigration laws tightened up considerably, immigrants required visas in order to enter the US, and the visa had to be procured from a US embassy in the immigrant's home country before starting their journey.
I have family that came from Lithuania to the US in the early 1920s. I actually found their ship passenger lists to contain more detailed information about their immediate lives in Lithuania, than the one internal passport application that I have found for another relative.
There are other family members that I have, who did apply for internal passports, but all that exists is a list on Jewishgen that shows they received the passports. I have also asked the Lithuanian archives, and they do not have the passport applications for these relatives. My takeaway is that over the years some of these applications were lost.
You could inquire directly on the Litvaksig website, with contacts there, about any other places that you might look for passport records.
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Michele Lock
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Rabinowitz in Papile, Lithuania and Riga, Latvia
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