By integrating Lightstreamer in your web application, your pages will be supplied by your application server while real-time data will be supplied by Lightstreamer Server directly to the client browser.
You can find an explanation of our philosophy in the Web Client Dev.pdf document under DOCS-SDKs\sdk_client_html\doc in LS distribution package.

Now that the tutorial demo is working, you can look at the preinstalled demos available from the home page of Lightstreamer Server and see the "External Deployment" section in the home page for hints on how the same demos can be redeployed by moving the pages to a web server and letting Lightstreamer Server only handle the real-time updates.
This should be the template for your own web application.

Hence, your Data Adapter running on Lightstreamer Server should be able to get any real-time data from your back-end, possibly bypassing the application server.