We never had the need for a door on the 'litter box room' until we got a new puppy. He seemed to think the litter box was a big bowl of "dog treats" for him to enjoy. Do I want to spend money on a door? Nope. Can I move the litter box to a new location? Not at this time. Do I want him eating poop? Certainly not. My solution?
I had a couple empty litter containers lying around, so when I bought a new tub o' litter I poured a little into each of the empties to create some weight. I then lined them in the doorway as a temporary 'blockade' so the puppy no longer has access to the litter box!
Right now the containers are in their 'pure form', but I do like the idea of spray painting them to match and then reusing them in the future