Link Controller v12.1 Link Creation error. no reply from big3d

Link Controller (LC) is a subnet of the larger GTM product (now known as BigIP DNS), and as such, it depends on a basic GTM configuration, which includes a data center (as you found out), and at least one GTM server object pointing to a self-ip on itself. It it through this tcp connection that it talks to (itself) via the big3d process, which runs all the probes

You'll need to create the gtm server object in tmsh, as there's no GUI method to do it.

create gtm server lc datacenter main addresses add {x.x.x.x}

Where x.x.x.x is a self-ip on the link controller that has an allow-service setting that permits connections to tcp/4353 (iQuery)