I have the 2004 LS430 with the Ultra package too. When I press "Height Hi", the car slowly rises. It take about 3 to 5 minutes to go up about 2.5 inches.
You can see the height change from right above the tire to the body itself.
The easiest way to "feel" the different is to change the height while the car is in park, dangle your left foot outside the car and touching the ground before you start. You should feel the car slowly rise.
As for sport suspension, you can notice the difference when going over dips. The change is not that dramatic, but if you drive the car enough in either mode over familiar roads (and bumps) you should notice the difference. You can also try it where there are speed bumps.
