I would like to join the same index elements of many different lists of lists and obtaining a list of lists of the joined elements.
The lists always have the same length. Here is an example much simpler to understand.
list1 = [[1, 0], [1, 0], [1, 0], [0, 1]]
list2 = [[2, 1], [2, 1], [1, 2], [3, 2]]
LIST = [[1,0,2,1],[1,0,2,1],[1,0,1,2],[0,1,3,2]]
Use a list comprehension:
Result = [item1 + item2 for item1, item2 in zip(list1, list2)]
It's is the same thing as this:
Result =  for item1, item2 in zip(list1, list2): Result.append(item1 + item2)
If you feel like this line is too long and a bit cumbersome, try this:
from operator import add Result = list(map(add, zip(list1, list2)))
If you're using Python 2.x, you can safely get rid of the call to
list in this example.