If you have upgraded to OS X 12.0 or newer and are using LockDown Browser for the first time, you will likely need to manually grant LockDown Browser permission to access your camera and microphone.
To do this, on your Mac go to: System Preferences > Security and Privacy > Camera
Then click the enable option next to LockDown Browser and/or LockDown Browser OEM, as shown in this photo:
Perform this same action for your microphone. Go to: System Preferences > Security and Privacy > Microphone
Click the enable option next to LockDown Browser and/or LockDown Browser OEM, as shown in this photo: