Sorry for lacking a step by step tutorial, we will add one later.
I think the step you missing is to configure a mount point of the LSAPI dispatcher. You can do that by either
To add a LSAPI context with URI: /dispatch.lsapi, using the LSAPI as handler.
To add a script handler for suffix "lsapi", using the LSAPI as handler.
I personally prefer the first approach. The Rails app should be ready to roll. :-)