Soon after acquiring Vexcalibur, you will receive a new questline titlted Vexcalibur: Authorization Override. Completing it will reward you with a Basic Authorization Mod that you will be able to slot into the Vexcalibur. It is a fairly short quest that can be completed fairly easily. In this Destiny 2: Lightfall guide, we have detailed everything you need to know about completing Vexcalibur: Authorization: Override.
Defeating Vex
For this step, you will need to defeat a few Vex. There are multiple places where you can do that such as Neomuna, Nessus, etc. Since the Patrol Zone in Neomuna is locked, we recommend repeatedly farming The Orrey (Lost Sector) on Nessus until you are done. It should take you 2-3 runs at most. If you like a challenge, you can always run Terminal Overload in Neomuna. There are multiple Vex that appear in the activity.
Basic Authorization Mod
After you are done defeating Vex, open your inventory, right-click on Vexcalibur, and insert the Authorization Override.
Return to the War Table
After you have inserted the Basic Authorization Mod, return to the H.E.L.M. and visit War Table. After listening to the message, you will be able to bypass the Security Walls scattered throughout the Avalon mission. We also recommend trying it out on the Legend difficulty if you are around 1820 and have a competent fireteam who can persist through.
This is how you can complete Vexcalibur: Authorization Override in Destiny 2: Lightfall. Also, feel free to see our detailed Destiny 2: Lightfall wiki for other guides.