Ok, of course - developer issues!
In Lucee Admin - the SSL Certificates – the mistake I was making, when checking to see if the CA existed, I was using the full endpoint: apitest.authorize.net/xml/v1/request.api
This always fails… Instead, using just the root url: apitest.authorize.net
Lucee lists the certs properly and I can then install the certs from this page.
Note that I also had to install the certs from: accesstest.authorize.net
UPDATE: This addresses the issue without having to download any certs via the admin:
Lucee rocks.