LOL!
Perhaps this page might give you a little idea? I know the pictures aren't very big, but at least it has "normal" (aka "green") cucumbers, "Continental" cucumbers and "Lebanese" cucumbers all on the same page. And it does certainly seem to be only part of the Australian dialect, since all nine results from Google Image for "lebanese cucumber" were from Australian sites. Though why one of the results was a picture of a tub of Philadelphia Spreadable Cream Cheese, I haven't the faintest... Ah, it's because the page was a recipe which included Lebanese cucumber and cream cheese, and the cream cheese was the only thing they had a picture of on the page. I suppose they specififed Lebanese cucumber for the recipe because it was a recipe for a snack, and therefore the smaller size of the Lebanese cucumber made it more convenient to use than a Continental cucumber.

A few more results:
this one has a description as well as a small picture,
this one has a bunch of other cucumbers to compare against (though they seem to have two types of "Lebanese" cucumbers).