LRU cache design using dict and doubly linked list
First off, the way you're commenting your functions is completely wrong. Proper commenting for functions uses Python docstrings. For example:

def my_func( ... ):
    """
    Write a description of your
    function and it's arguments
    here.
    """
    ...


Secondly, according to Python's official style guide, PEP8, your naming is incorrect. Variables and functions should be in snake_case, and classes should be in PascalCase. If the variable is a constant, it should be in UPPERCASE_SNAKE_CASE.

Finally, why do you have Node as a subclass of LRUCache? Why can't Node be a top-level class? I see no reason it shouldn't be.