I would work my way back starting with the 1940 Census and work backwards. You could try to find your great-grandtaher and his family in the 1920 Census if you were pretty sure about where they lived and their ages and such.
The problem is that they may have been using a variation of their Lithuanian surname at that point.
Do you know where your great-grandfather was born? He likely was baptized and the church record might have his parents names with their Lithuanian spelling. Any idea asto what church he was baptized in?
You can see why staring with the 1940 Census and working back might be easier as a starting point.