Richard Lugar actually said...

Senator Harry Reid, now the Democratic majority leader, did not find it convenient to take up the treaty.

Lugar notes Reid's decision not to advance the Law of the Sea treaty.

05/22/2012

More Richard Lugar Quotes

The Senate should enthusiastically affirm the leadership of the United States in this vital area of international relations by giving advice...

The Commander in Chief, the Joint Chiefs of Staff, the United States Navy, the United States Coast Guard, and individual combatant commander...

Consequently, the United States cannot insulate itself from the Convention merely by declining to ratify.

It does raise the points which you have made that it is not really clear just in terms of law enforcement.