Open Cortana (Shortcut: Windows key + S) and go to Settings.
Turn on the option for "Let me use Cortana even when my device is locked."
You can also let Cortana respond to "Hey Cortana," but it's not mandatory.
I installed the anniversary update and everything is working smoothly except for cortana. It works fine from task bar but even after enabling it on lock scsreen in cortana settings , it refuses to show on lock screen. Has anyone else experienced this?