Ed,
A wake-up signal can come from any HDMI connected device across the entire setup. You can try removing each component in turn and testing to see whether the issue happens. Look for any CEC settings within your other components (Blu-ray players, game systems, etc.) to see if they can be individually adjusted or disabled. However, since the "TV" source is the one that comes up when the system turns on in error, experience says that disabling the TV's HDMI CEC options will be the simplest way to resolve this.
If you program your Bose remote control to operate the TV by IR codes instead of via HDMI CEC, then turning this off will be less of an issue. Codes for LG will be listed in the documentation that came with the system.
You can also download that code list from this page.
For instructions on programing the remote,
please follow the steps in this video.
Thank you.