Update to Cortana for Android adds lock screen support
If you already have Cortana installed on your Android phone, you can get the update by opening the Google Play Store and clicking on the hamburger menu on the left of the Google Play search bar. Click on My apps & games and scroll down to Cortana. Click on "update," and the job is done. If you don't have Cortana installed on your phone, open the Google Play Store and click on Cortana using the search bar. From there, you should be able to install the virtual personal assistant on your handset.
Ironically, the Cortana update comes the same day that Google Assistant starts rolling out to all Android models powered by Marshmallow 6.0 or higher. Assistant gives Google a little more personality by making the AI voice activated personal sidekick more conversational.
source: Cortana (Android|iOS) via AndroidPolice