Real time monitoring...

The Lawson (free) mobile system monitor helps monitor the environment and underlying OS (via Sigar plugin).
I have installed/configured it, but haven't used it extensively so I can't vouch for how reliable it is.
Since it's typically installed on same server/WebSphere instance as LSF -- it's probably not going to be that helpful if the server goes down...
For that you really need something that runs outside the LSF infrastructure.

One product that seems to do a decent job and that covers most of your needs (although they don't have a module specific to Lawson):
http://www.solarwinds.com...ication-monitor.aspx
For Lawson-specifics you can set up port / response time monitoring, do periodic GEN DB table scans for stuck jobs, etc.

Or you can implement both, and rely on Solarwinds for the infrastructure monitoring and the Lawson monitor for the environment itself.