Determine if one string is a rotation of the other Python
Good work! This is certainly primarily an improvement from your previous implementation. However, there are still a few problems. 


Don't raise an error when passed two lists of differing length. Not only is this unexpected by users, it breaks some of your tests. 

# 1 empty, 1 not empty
lst1, lst2 = [], [1]
assert not is_rotated(lst1, lst2)
lst1, lst2 = [1], []
assert not is_rotated(lst1, lst2)

The pattern of if condition return True else return False should be replaced with return condition. This is easier to read and reduces the amount of code you have to write!
Joining the lists of integers with the empty string as a separator is dangerous. If I pass in [1, 23] and [12, 3] the function will incorrectly return True. If the function only has to handle integers, you can easily fix this by using a comma (or any other character) as a separator. (Just remember to include it when checking if the string is contained in the other string str1 + ',' + str1)


I would prefer a more general solution that works for lists containing any type of element. Using Nas Banov's answer from Stack Overflow to handle the sub list check, this is a really simple function to write.

def contains_sublist(lst, sublst):
  n = len(sublst)
  return any((sublst == lst[i:i+n]) for i in range(len(lst)-n+1))

def is_rotated(lst1, lst2):
  if not len(lst1) == len(lst2):
    return False
  return len(lst1) == 0 or contains_sublist(lst2 * 2, lst1)