I have created a more general function, that sorts more than two lists based on another one, inspired by @Whatang's answer.
def parallel_sort(*lists):
"""
Sorts the given lists, based on the first one.
:param lists: lists to be sorted
:return: a tuple containing the sorted lists
"""
# Create the initially empty lists to later store the sorted items
sorted_lists = tuple([] for _ in range(len(lists)))
# Unpack the lists, sort them, zip them and iterate over them
for t in sorted(zip(*lists)):
# list items are now sorted based on the first list
for i, item in enumerate(t): # for each item...
sorted_lists[i].append(item) # ...store it in the appropriate list
return sorted_lists