When inquiring about the watch, the LG staff continued to tell me the security capabilities of the watch with the caveat of this accessory or that accessory. A device lock option can be used with a voice command through a Bluetooth gadget. A privacy keyboard can be used to secure login. Finally the LG rep said there is a privacy pin code option that can be operated from the watch itself -- needing no accessory. At the moment, Android Wear 1.0 does not have any security features such as a lock code, for example.
However, there are several third-party applications for Android Wear on the Android Wear Store that can do this. Takeaway: Do your research first on this device before diving in!