Many users of the Moto G smartphone have reported issues with LED notification. They have reported that the LED notification does not ever turn on, irrespective of whether they receive incoming emails, texts, calls, etc.
It is thought that the issue may occur due to restoration of setting from a Google account. Such an account may have instructions of the older smartphone where the notification feature was either not available or turned off.
Resolution: The problem is well known and Motorola is aware about it. They released a widget called Notification Light Widget as a fix for the LED notification issue. Users may download the widget from Google Play Store, set it on the home screen, and then toggle it to turn it on. You may later delete the widget; it will not affect the working of LED notifications.