Hi Liza,
My family name is Lubotsky. Many of the earliest records of Lubotsky/Lubotzky/Lubocki that I've found were located in Lithuania, esp. Vidzy, in the1811 Revision List. Later in the 19th century you can find records in other countries. Mine ancestors likely moved from Lithuania to what is now Belarus, before moving to the United States. Not sure if this will be helpful to you, but happy to chat more.
Darren Lubotsky
Chicago, IL USA