Here is how it goes:
1. First lift checks if request is to be dealt with Stateless dispatch. If yes then serves immediately, else it moves on to point 2.
2. It checks if request is to be dealt with State-full dispatch, if yes then serves it in that particular fashion, else moves on to point 3.
3. Checks whether this request is a Comet/Ajax request. If yes then handles with Comet/Ajax handlers, else moves on to point 4.
4. Checks SiteMap to see if the request is valid or not. If yes then moves on else gives a 404 not found response.
Let me know if its still unclear.