Sorry, I could have made a more explicit mentioning of the javascript document.domain property.
Hence, the "domain setting" is a javascript feature and setting the domain to a value, like "lightstreamer.com", means issuing
Code:
document.domain = "lightstreamer.com";
According to the previous post, in order to have Lightstreamer working on Firefox in your scenario,
both your Push-page and Lightstreamer-generated data page should, in principle, issue:
Code:
document.domain = myHostname;
where myHostname is the name with which you access both the Web Server and Lightstreamer Server.

But note that you have no control on Lightstreamer-generated data page.
You can achieve all the above by using the setDomain method from Lightstreamer API, i.e. issuing:
Code:
pushPage.context.setDomain(myHostname);
which both sets the domain on the local Push-page and makes the LS Server do the same on its generated data page.