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I hunted down a reference to the lotus posture in the Satipatthana Sutta where it is stated in passing, as a matter of fact; so it is likely the lotus posture was one of those very obvious things to Indian yogis of the time that doesn't need much specific mention.
Nisidati pallankam abhujitva ujum kayam panidhaya parimukham satim upatthapetva so satova assasati sato passasati = "Sits down, bends in his legs crosswise on his lap, keeps his body erect, and arouses mindfulness in the object of meditation, namely, the breath which is in front of him. Mindful he breathes in, and mindful he breathes out."
And, as I already mentioned in the comment above, according to Hindu scriptures and yoga manuals the advantage of the lotus position is that it is self supporting. In arupa-jhanas (also well known and practiced by Hindus) when one has lost all sense of the body and mind, a lotus posture will ensure one doesn't fall over.
This doesn't specifically mean the Buddha sat in this posture under the Bodhi tree, but if he's advising others to do so, it is likely this was how he sat always.