Try the diagnostics menu and see what faults come up... (the following is for UK spec but I think they are very similar)
To access the Diagnostic Menu on the touch screen do the following.
1. Gear selector in park.
2. Handbrake on.
3. Ignition to ACC, (or start the engine if you want to do a speed check etc) wait for navi screen to power up, click "I Agree" (or buy the Vias Ipod or dvd lead and it does it for you)
4. Press and HOLD the OPTION button and AT THE SAME TIME...
5. Turn headlights from off to sidelights five times i.e. off/side/off/side/off.
6. To exit the menu, turn off the ignition, car will then behave as normal.
You will then get this screen displayed, it shows if there are any faults stored in the ECU, mine below I presume means there are no faults...
If you press Menu you will go to this screen
Follow your way through the options and you get more screens,
This one shows satellites locked onto, and location etc
There is one to test all the buttons (I'm pressing the AUDIO button here in case you didn't guess!!)
This one shows battery, speed, ignition, lights and parking brake.
These next two check colours
These next two allow you to test the touch screen, I have touched the first 5 bars on each one (sorry the second is a bit out of focus)
Vehicle signal and sensor test. If you start the engine instead of just switching the ignition on you can drive away and check your speed via the sat nav in MPH or KPH
I don't think there is anything you can mess up in looking at this but please do it at your own risk, I have played with mine a few times now with no ill effects.
This is for the 2001-2003 LS430. The later cars will be a bit different but I think the access method is the same
I don't know what any of the fault codes would be but maybe a Google of them would help....