They're actually pretty easy to make. There are a million recipes online, and you can even use store-bought cake or cake mix. Then dip squares in chocolate and roll in coconut. Even in Australia, where they're sold everywhere, a lot of folks just make them at home.
Otherwise, there are places online that sell commercial lamington's from Australia (e.g.,
https://theaustralianfoodshop.com/)
But, alas, know of of no local stores that sell them.