Galadriel created Lothlorien through the power of her ring, Nenya. When the One Ring is destroyed, the 3 rings (and the others) lose their powers, so Lothlorien will fade.
Then the Elves have a choice (or atleast certain elves), of travelling into the West (like Galadriel, Elrond, Celeborn, Legolas...etc) or staying in middle-earth. If they stay in middle-earth then yes they will end up fading away.
P.S. Good observation

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