Cortana will soon be accessible from the Android lock screen

Furthermore, this feature doesn't override your current lock screen, meaning that you can still use it on your device's stock lock screen or a custom one, like Microsoft's own Next Lock Screen.
If you don't feel like waiting and want to try out Cortana on your lock screen right now, you can enroll in the beta program by following the link below.
source: Microsoft via MSPoweruser

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