The LS 500h does have an EV mode that can get the car going at slower speeds when feathering the throttle pedal. However, when dipping even a little deeper into the right pedal, the gas engine quickly fires up.
The benefit of you getting a hybrid LS over the normal gas model is better fuel economy. With all-wheel drive, it returns an EPA-estimated 23 miles per gallon in the city and 31 mpg on the highway. That betters the gas-only LS 500's 18 mpg city and 27 mpg highway figures.