your logic seems to be impeccable. In that case, I would pour over maps and gazetiers of "Minsgyberna" in search of a place the begins with "Li". People tend to catch the first syllable accurately.
My rational behind "Lida" was that the enumerator Mrs. Koplowitz was most likely an immigrant himself, knew Russian, and inadvertently substituted English 'd' for Russian 'g'. Both letters record the same sound - but in different languages. A phrase such is "Lida resident" would be written as "Ligskij meshchanin" in Russian.
FAST Genealogy Service