Consumer Electronics Control (CEC) allows certain HDMI devices to control each other when appropriate. Enable CEC and configure sleep settings in Preferences > Video.
If your display does not fall asleep when your Lifesize Icon video system falls asleep, CEC is incompatible with the display.
If an incoming call wakes a sleeping video system, check whether the monitor wakes up within a reasonable amount of time. If it does not, the monitor probably requires too much time to power up for CEC to be useful.
In scenarios like these examples, consider using analog speakers instead of the display speakers.