This LockDown Browser-Mac error is similar to the LockDown Browser-Windows error discussed in the knowledgebase article, "Update server connection is blocked or not available".

When LockDown Browser starts, it must be permitted to access this server: static-public-downloads-cloud.respondus.com

LockDown Browser accesses this server in order to check if an update has been issued by Respondus. If your computer and/or network is blocking access to this server, the LockDown Browser session will not be permitted to continue.
It's possible that your computer's security settings are blocking access, or you possibly have a firewall or anti-virus software running on your computer or network that is causing the block.

What to do next:

1) Temporarily relax all anti-virus and firewall software on the computer and try the exam again. 

2) Your computer, ISP, or network may be blocking access to the Respondus servers. These servers include:

server-profiles-respondus-com.s3-external-1.amazonaws.com
static-public-downloads-cloud.respondus.com
www.respondus.com
help-center-respondus-com.s3.amazonaws.com
smc-service-cloud.respondus2.com

These domains may need to be added as "trusted sites" in security settings on the local computer and may need to be added to network firewalls or routers. For Macs, you should check settings in System Preferences-Security & Privacy.

3) We also recommend doing a complete power down and restart of your Mac.

4) For Macs, the "a4 error" can be due to permissions issues with the specific user account on the Mac. Some students have found creating another user account with "Allow user to administer this computer", restarting the Mac and logging with the new user account allowed them to start LockDown Browser.