Firefox 1.0 is affected by a bug that prevents to issue any XMLHttpRequest' afrter the document.domain has been set, even to the original domain.
See Bug 290100 at
https://bugzilla.mozilla.org/show_bug.cgi?id=290100.
This bug does not casue any issue to Lightstreamer. But if you perform your own XHR calls together with Lightstreamer (that sets the document.domain), you will see a security exception in Firefox 1.0.
You can find a workaround at
http://fettig.net/weblog/2005/11/28/how-to-make-xmlhttprequest-connections-to-another-server-in-your-domain/.
This bug has been fixed in Firefox 1.5.