The lion is one of the most heavily used animals in Indian religious imagery. Simhasana as a word means lion seat, and outside the yoga literature it is the ordinary term for a throne, the lion supported seat of a king and of an enthroned deity or Buddha. Buddhist texts speak of the lion's roar as the figure for authoritative teaching; Vishnu's fourth avatar is the man lion Narasimha; Durga rides a lion, and Jain and Buddhist thrones are carved with lions at the base.
The posture name sits inside that field. A reader meeting simhasana in a hatha manual would already know the word as the name of a throne, and the manuals do not comment on the overlap. The atlas records the double sense without asserting that the compilers intended the royal one, because a shared word is not by itself evidence of an intended reference.
What can be said is that the corpus is comfortable using words that carry weight. The lion seat, the lotus, the thunderbolt and the auspicious all name postures with terms whose other lives are royal, iconographic or cosmological, and none of the manuals stops to explain any of them. A technical vocabulary built out of a shared religious vocabulary is not neutral, but it is not argued for either, and reading intention into it beyond what the texts state is a step the atlas declines to take.