KINGSTON SOUTH EAST, Australia — On a grassy patch of land beside the Princes Highway, Casey Sharpe sighed as he looked up at his most prized and problematic possession: a 55-foot-tall spiny lobster.

His name is Larry. And his future is uncertain.

The crowds Mr. Sharpe imagined when he bought Larry, known as The Big Lobster, 11 years ago never materialized. The business behind Larry’s tail closed two years ago.

Now, a tempting offer has arrived that would cut Mr. Sharpe’s losses and take Larry off his hands. The catch? Larry would be shipped thousands of miles away to Western Australia.

Mr. Sharpe’s deadline for the local council — or someone else — to save the lobster is next Monday. And if Larry leaves, neighbors will not be happy.