If you compare the design of Omashu to the design of multiple lion turtle cities, they both appear to be very stacked cities, with buildings across all different heights. They're both circular cities as well.

The origin tale of Omashu dates from around the conception of earthbending, which we now know to be about 10.000 years prior to Korra's time (aka Wan's time). Oma, the woman from the story, is said to be the first earthbender. Lion turtles granted people the ability to bend, which both Oma and Shu used to make the secret tunnel leading to and away from the city. The difference is, Oma and Shu learned the technique from badgermoles, which is why they were considered so powerful. (Just like Wan, who learned from the dragon during his time away from the city).

There's a very real possibility that there was a war within the turtle city (we saw all the class problems in Wan's city, and humans are gonna human) and in order to escape the war, Oma and Shu asked the turtle for earthbending so they could escape and be together safely.

On the avatar wiki, it also explains that after the era of the spirits, during the era of the Avatar, the lion turtles got hunted into near extinction. Some turtles chose to hide, like the turtle Aang came across in the show who chose to pose as an island. Earth lion turtles are able to bury themselves into the ground. Omashu could very well be an earth turtle that's buried underground to hide from society, and because so much time has passed history turned into myth.

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