"How to dynamically set the length of a Python dictionary (i.e. how to dynamically set the number of key values in a dictionary)"
"And each value (which will be an integer) of the dictionary should point to a list."
First of all, key values above in the first sentence are called simply keys in Python. Second, the things to which these keys "point" are called values. So, your lists are values.
To answer your first question: you can't set the length of the dictionary. Instead you simply add key-value pairs to the dictionary (or delete keys) and this is how you dynamically control the length of the dictionary.
What you really want, it seems to me (after some head scratching), is a defaultdict
:
In [32]: from collections import defaultdict
...: d = defaultdict(list)
...: d['first'].append(1)
...: print(d['second']) # simply accessing a non-existant key
...: # creates the default value - an empty list
...: print(d)
...:
[]
defaultdict(<class 'list'>, {'first': [1], 'second': []})