In New Zealand, isn't there also a huge insect called the Weta? I've never been to your beautiful homeland, but I've heard tales. I wonder what exactly differentiates these "tree lobsters" from Weta.
Weta are a bit like large, nocturnal crickets. There are more than one variety, but you're probably thinking of the giant variety.
We get a relative of them here in the US, usually called cave crickets or camel crickets (here in VA).