How do I connect my EX-HDD connected to my AirPort Extreme to my LG Smart TV?

In order for your TV to access an AirPort Disk it would require some sort of file browser client that is capable of accessing a network drive via either the SMB or AFP file sharing protocol. This is how your Mac and other laptop does it.

I would suggest that you post your question at the LG support site to see if they offer something like this as an app for their smart TVs.