Nitrous.IO does not currently support websockets out of the box, so LiveReload will not work without some tinkering.
As of the time of writing (July 11, 2013), you need to forward a port through an SSH tunnel in order to connect to websockets on your Nitrous box. Instructions for setting up SSH to your Nitrous box can be found on their support site.
(I used port 3000 for my web server, since it is one of the ports Nitrous makes available by default, and the default port 35729 for LiveReload. Substitute the ports you're using in the instructions below.)
Forward local port 3000 to localhost:3000 and local port 35729 to localhost:35729.
I used PuTTY, and it looks like this:
Even though port 3000 is accessible outside the tunnel, we need to forward it and load the page through the tunnel, so that the client-side LiveReload snippet will open its websocket through the tunnel as well.
Now open localhost:3000 in your browser, and you should be able to view your site with LiveReload.