Check the dates, when there were this Genoese community and thousands of Europeans. I don't know for sure, but most likely it was after sea road to China. Lithuania has to do with it, because it was pagan country, hostile to Christian Europeans that took territory between Western Europe and China or Mongolia. Middle east was controlled by Ilkhanate, Central Asia by Golden Horde these two were hostile. Lithuanians were hostile to Golden Horde. Where is this magical way to China?