According to Wikipedia's page on the law of the land which cites Black's law dictionary for the current meaning, the expression always meant the law on the land on which it was passed.
It refers to all of the laws in force within a country or region, including statute law and case-made law.
In the year 1215, this term was used in Magna Carta. Perhaps the most famous clause of Magna Carta states:
No Freeman shall be taken or imprisoned, or be disseised of his Freehold, or Liberties, or free Customs, or be outlawed, or exiled, or any other wise destroyed; nor will We not pass upon him, nor condemn him, but by lawful judgment of his Peers, or by the Law of the Land.
This is sometimes called the "law of the land clause". Magna Carta was originally written in Latin, and the Latin term is lex terrae, or legem terrae in the accusative case (i.e. when the term is being used as the object in a sentence).
Half a millennium later, following the American Revolution, legislators looked to Magna Carta for inspiration, and emulated its "law of the land" language. Versions of it can be found in the Virginia Constitution of 1776, the North Carolina Constitution of 1776, the Delaware Constitution of 1776, the Maryland Constitution of 1776, the New York Constitution of 1777, the South Carolina Constitution of 1778, the Massachusetts Constitution of 1780, and the New Hampshire Constitution of 1784.
The only disputes were around how much of the laws on a given land were implied by this expression, but these precede the US stuff, e.g.
English jurists, writing of legem terrae in reference to the Magna Carta, stated that this term embraces all laws that are in force for the time being within a jurisdiction. For example, Edward Coke, commenting upon Magna Carta, wrote in 1606: "no man be taken or imprisoned but per legem terrae, that is, by the common law, statute law, or custom of England." [...]
Littleton Powys, a judge of the King's Bench, wrote in 1704 with reference to Magna Carta: "lex terrae is not confined to the common law, but takes in all the other laws, which are in force in this realm; as the civil and canon law...." In 1975, political scientist Keith Jurow asserted that the term "law of the land", as understood by Lord Coke, includes only the common law, but that assertion by Jurow was called "manifestly wrong" in a 1990 article by Brigham Young Law School professor Robert Riggs.
So I don't see any evidence it ever meant something else in the US. The parallels with the law of the sea seem a red herring to me.