Android 5.1.1 Lollipop is a pretty big update for Android Wear smartwatches, as it comes with support for always-on apps, the ability to draw emojis, as well as new navigation gestures. Sadly, the most important new feature in the new Android Wear version, Wi-Fi, will not be enabled on the Asus Zenwatch. Note that this not a slip on the behalf of Asus software engineers. Wi-Fi will not be enabled on the Asus ZenWatch because the wearable lacks Wi-Fi radios.
As with all Android updates, 5.1.1 Lollipop will gradually roll out to Asus Zenwatch owners across the globe, meaning that it may take a while before your device gets the OTA update. Your smartwatch will bring out a notification when the update is available for your device, as it routinely checks for new software updates once every few hours. These are the steps that you should take in case that you want to manually check for updates: swipe down on the watch face -> swipe to Settings -> About > System Updates.
If you can't wait for the OTA to reach your device, you can download the Android 5.1.1 Lollipop OTA for the Asus Zenwatch from this link.