Unless there is information that says the lobster was caught in the United States, spiny lobster is not sustainable.
U.S. spiny lobster stocks are not overfished. However, stocks in South America are extremely overfished. This is due to the high economic importance and market value of spiny lobster. Many remote coastal communities rely on the fishery for their livihoods.
Combined with the fact that spiny lobster are easy to catch and management in South America is not enforced well, this species is heavily overfished.