Lyse has actively been a Scion for 6 years. This was for me the important detail from my character's perspective. My WoL, indeed any WoL, would have never met Yda. For all the false names, Lyse has been a comrade to the other Scions for a decent length of time at this point. Also remember that Lyse would have grown up knowing quite a few of them, if not well. She certainly would have known Y'shtola since Y'shtola was a close friend of the original Yda.

As Y'shtola says at the end, she is a comrade. She has long since earned her stripes in that regard.