Microsoft is currently in the process of testing Cortana functionality on Android lock screens. To be part of the testing, you do need to sign up to the Cortana for Android beta program as that is where the new updated version of Cortana is currently available. Although, as with all things beta, providing there are no monumental or significant issues, it is expected that Cortana lock screen functionality will hit the standard (non-beta) version of Cortana for Android in due course. On a side note, it does also seem as though this latest version comes with a number of small improvements including the ability to change Cortana's color in Settings and an improved retrieval speed.
What is interesting about this particular feature is that it does not seem to override or replace your current lock screen. Which means you can run any lock screen you want but still make use of Cortana in the background. Once the device is locked, the Cortana 'ring' is present and swiping the ring (while in locked mode) will allow you to interact with Cortana in the usual manner. All this new feature does, is essentially add a shortcut to Cortana to your existing lock screen.
Of course, the benefit to Microsoft with this sort of implementation is that it allows users to access Cortana before you unlock your smartphone and head to Google's own digital assistant option. Which might result in more people starting to use Cortana in the future. The coupling of this quick access with the fact that you do not need to actually make use of a Microsoft lock screen to access the feature is also likely to be additionally beneficial to Android users, as they are not compromising on one form of customization for Cortana functionality. Which in turn, might also prove to be a motivator for some to try out Cortana. If nothing else, if you're already a Cortana user, then this new feature will certainly provide you with a much quicker way to make use of Cortana going forward. You can find out more or join the beta and check out Cortana on your lock screen through the link below.