Lothlórien.
Lórien.
Lórinand.
The land of the golden trees between the Eastside of Hithaeglir and West of Anduin at the Northbrink of river Celebrant and South of the outlayers of Fanuidhol. In size North/South about 40 Miles, East/West around 75 Miles. An area of Lothlórien is called the Naith. The Elvish city in Lothlórien is called Caras Galadon, besides this is there the place named Cerin Amroth.
The story of Lothlórien goes way back in history before Celeborn and Galadriel entered the land and the natural inhabitants of the area are the Silvan Elves. These Elves descented from the Lindarin Elves lead by Dân ( became overall known as Teleri / Moriquendi -> Nandor -> Silvan-Elves ) who abandoned the Great March to Valinor and never went Westward or crossed Ered Luin but lingered on the shores of Middleearth and established small realms along the shores or in woodlands far from the sea.
The speech in Lotlórien was generally Telerian ( became blended with Sindarin throughout the ages ) in the end of the 3 age not much of their "own" language remained but some of the placenames is of the Silvan tongue and can be seen in some of the names; Caras Galadon and the name of the land itself Lórinand is of the Silvan tongue but after the arrival of Galadriel who was of Noldorin ancestry the Noldorin and Quenya speech were learned and were used at least in the household of Celeborn and Galadriel.
Exactly when Lórien became a realm in the meaning of an ( nearly ) clearly bordered area with a ruler is not known but the names in the Silvan speech indicates it was before Galadriel and Celeborn entered the land. But some clues can be extracted; in Southern Mirkwood around Amon Lanc lived in 1 age an Elvish king Oropher, also of Silvan origin, and it is told he had friendship with the Elves in Lórien but he withdraw North in the beginning of 2 age due to the increase of Dwarves in Moria whom he did not like. This tells us that Lórien existed as a defined populated area at this time. The borders was in East Anduin, West it was Dimrill Dale in Hithaeglir, Northern and Southern borders are more undefined, the Southern was in general Silverlode but the Elves claimed to govern the land deeper south into Field of Celebrant.
Of a King or Queen before Galadriel and Celeborn ( Who never took the title of this ) not much is clear.A old tale tells of Amdir who was a King of Lórien and had a son named Amroth but Amroth is in later tales told to be a son of Galadriel and Celeborn.