What is the virtue of running a Django application on Tornado over Apache or lighttpd?
Mainly, I wanted to make sure Tornado integrates with existing frameworks so that more people can play with it, and the separable parts are useful to people who don't want to use the whole Tornado stack.
Seriously, having a self-contained server is often nice, and the async support would be useful if you need to do long-polling or make http requests to other sites (e.g. making an API call to Facebook or Twitter).
Providing a way for Django to do the long polling, streaming, comet type aspect of it would be the next step, which I'm not sure Django can handle out of the box without a lot of changes. I hope someone makes it though.