I have realized that you started from the tutorial demo.
Note that the tutorial demo is based on Lightstreamer Server itself as the Web Server. If you now use an external Web Server, then the domain setting becomes important and has to be set properly.
An improper setting of the domain may also lead to browser-dependent issues.
Assuming you are using LS 3.4.8 (in the current 3.5 version the tutorial has been replaced) you can find instructions about the full deployment associated to the demos in DOCS-SDKs/sdk_client_web/examples. See StockListDemo/README.TXT, for instance.

Note: in LS 3.5 the same instructions are reached in a different way and are in
pages\demos\HOW_TO_DEPLOY_ON_YOUR_WEB_SERVER.TXT