The point of the difference between Yda's and Lyse's character was the Lyse was essentially pretending to be "someone else" the entire time we knew her. That someone else is "Yda". Once Papalymo dies, Lyse finds out everyone knew she wasn't Yda anyway. So she stops pretending to be "Yda" only to realize that she no longer knows who she is as "Lyse.

Stormblood is Lyse figuring out who "Lyse" is. In fact, 4.0 is framed with Lyse narrating the events to her inner Papalymo. Lyse is telling her best friend how she figured out who she truly is when she's not faking being someone else. It's also good to remember that for all of Stormblood, Lyse is dealing with her best friend's death. No matter who she is, Lyse would always be more subdued because of that. If Lyse didn't change when Papalymo died in some way, I'd think they're relationship wasn't as genuine as it came off. Deaths that don't effect characters are as fake as deaths that aren't permanent.