Will my Velocity Gold membership allow me access to Etihad's lounge even if I booked my economy flight on Etihad's website?

I’ve booked an economy flight on Etihad through the Etihad website. Am I still entitled to use the Etihad lounges with my Velocity Gold membership even though I didn’t book the flight through Virgin Australia with a VA flight number?

Yes is the short answer. You can access the Etihad lounge in Sydney as long as not travelling on the A380 - if so then you get access to the new Air NZ lounge instead as the Etihad lounge gets too busy. Other cities in AU you use whichever lounge Ethiad has a contract with. In Perth it is a QF lounge!

In Abu Dahbi you get access to the Al Rheem lounge - NOT the  Ethiad Business lounge.

On the return leg you access the Etihad lounge from wherever you are travelling to.