Eirika was being Wrong Genre Savvy when she gave the Sacred Stone to Lyon.More specifically, she's been told by numerous sources that Lyon's salvation is an Impossible Task. Since this is fiction, you expect her to be able to do the impossible and, naturally, save the day with The Power of Friendship. It gets averted.
Both versions of the Demon King's possession are canon at the same time.At first, it seems weird that Lyon's level of control is so vastly different between routes. However, it would make sense if Fomortiis was deliberately changing things up depending on who he's talking to, and it's even more logical when you look at each twin specifically. He lets Lyon think he has more control when talking to Ephraim because he knows that Lyon was jealous of him, while he takes more control over Lyon when speaking to Erika to play off her sympathy. Basically, Fomortiis never had "less" control in Ephraim's route; he's just messing with Lyon and both twins in different ways.