in what today is known as belarus there were chasidim, in what today is known as lithuania, as far as i know there werent any chasidim
As pointed out, the borders and the names were pretty fluid throughout history (and Yidden living in actual Russia is a later development than in Belarus, Lithuania, Ukraine, etc.)
The Alter Rebbe was known as the Rav from Ladi or Liozna, both towns in what was known as רייסין. You might have heard of רייסין bunched together with ליטא when it comes to מנהגים (slichos comes to mind כמנהג ליטא רייסין זאמוט). Many places in current Belarus you would consider of Jewish Lithuanian ethnicity: Grodno, Lida, Minsk just to name a few showing up on the map below.
Look at some of the maps here
http://www.lithuanianmaps.com/Maps1777-86.html and you will see these areas as part of Lithuania.
For example, see
not really, but id be happy to hear...
The Maggid's family had a
מגילת יוחסין going back centuries (I'm not sure how far back, but IIRC back to גאונים, possibly even אמוראים or תנאים). At a certain point that megilla was lost to a fire. The Maggid's mother was very upset about it, so her son told her, don't worry, we will start a new Yichus from me.
After the Maggid passed away, territories were divided amongst the talmidim to spread Chassidus. The Alter Rebbe was given Russia and Lithuania IINM.
I'm sure
@Freddie and others can give more accurate details of the stories.