Not everyone gets Echo flashbacks--that appears to be the WoL's 'echo gimmick', like how Krile's (and probably Fordola's, she doesn't describe it well) is sensing aether, Zenos' (and the Sahagin Priest's) is possession, and Mikoto's is future sight. So... no, Fordola can't plausibly have seen Lyse's memories of Yda, because she can't see memories at all.
So it's reasonable to assume this will probably never come up. Lyse and Fordola are aware of each other, but aren't on 'speaking openly about probably irrelevant parts of their history' terms. And hell, we don't even know how common the names 'Lyse' and 'Yda' are; from our perspective we recognize that a fictional world only has double-up names if somehow appropriate, but to them? Maybe 'Yda' is the Ala Mhigan equivalent of, like, 'Claire' and you meet so many that learning that someone's sister's name is super normal.