Yes, generally speaking, separation of concerns is always a good architectural pattern. Lightstreamer has been designed and optimized for asynchronous (pub/sub) communication, while Web servers have evolved for synchronous (request/response) communication. Usually the two servers sit along in full synergy, each one taking care of the aspects it is specialized for.

That being said, there can be cases where you might want to leverage Lightstreamer even for request/response. Perhaps because you want to keep all your server-side logic inside a single adapter, or because you need a law latency link to send messages from the client to the server. With XHR, you might stumble into connection setup latency (especially high with SSL), while with Lightstreamer the link is kept always open, reducing round-trip latency.