Well, first off, I'd say it is debatable whether or not Lulu is a vanity press or a self-publisher. I would classify it as a vanity press. It makes its money primarily from selling books to the author and the author's friends.
As for when it would be a right decision to go with self-publishing or a vanity press over a traditional publisher, there are many different reasons. If someone wanted to write a family history and put it in book form, or the history of a small town, or a historical event with regional interest at best, or was using the book as a form of extra income coinciding with their work -- such as someone who does customer service speeches to corporations writing and selling a book to sell to those companies.
Those are all areas that probably would not appeal to a large publisher, but are perfectly valid reasons to go ahead with vanity or self-publishing.
Why choose vanity over self-publishing? Well, first, as I mentioned, part of it will be a matter of what one considers vanity and what one considers self-publishing. If we wanted to be very strict about it, self-publishing would be contacting a printer whose sole business is to print books, not sell them. Anything else would be inching closer to vanity press.
But, for a short answer: When the fee is worth the service. If someone sets up their own publisher and charges $250 to publish with them and they use Lulu.com as their printer/distributor, then they fall pretty much into vanity publishing. And for someone that thinks $250 is not much to pay for getting a custom cover done and having someone else format and submit the book, it might be a great choice.
There are plenty of people that could spend hours on Lulu's site trying to figure out how to properly format the manuscript even if they are just using the clipart templates for a cover. Others could do the same in under an hour. In the end, it becomes a service.