“My father’s father was kennelmaster at the Rock. One autumn year, Lord Tytos came between a lioness and her prey. The lioness didn’t give a shit that she was Lannister’s own sigil. Bitch tore into my lord’s horse and would have done for my lord too, but my grandfather came up with the hounds. Three of his dogs died running her off."
Éowyn says that women must ride now, as they did in a like evil time in the days of Brego, when the wild men of the East came from the Inland Sea into the Eastemnet. - The History of Middle-earth, Volume 8, The War of the Ring*
* There we have a reference to the women of Rohan fighting against an invasion of Easterlings during the reign of Eorl’s grandson (named there as Brego, but following later versions this would be Aldor). This invasion would have been about four hundred years before Éowyn’s time.