After the Windows 10 Anniversary Update, Cortana is enabled by default on your lock screen if you haven’t disabled it entirely. If you don’t want Cortana to answer your questions when your PC is locked then it is a simple enough process to disable it.
Open Cortana button on your taskbar, simultaneously pressing Windows button + S on your keyboard. You can also activate it by simply saying “Hey Cortana” if you have it enabled. When Cortana is opened, click the Settings button.
On the Settings page, scroll down and turn off the “Use Cortana even when my device is locked” option.
There is no other way to access Cortana on the lock screen except by saying “Hey Cortana” into the microphone. Mobile users can access it by hitting the Search key to start her up. Also, Cortana can reply to many requests–like playing music or answering basic questions–right from the lock screen. However, if you ask Cortana to do something that involves settings or an app, Windows will ask you to sign in before Cortana can complete your request.