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The reasons of his mysterious wellness and relax are multiple, but they don't really come from the fact he is with Christoph.
Sure, she contributed to it, but her care isn't everything.

His amnesia kind of 'resetted' him to the moment he left his time.
When he woke up, the last memory he had was his mother's guards pushing him through a mysterious portal he had no idea where it would lead to.
As soon as he opened his eyes, he could tell that the symptoms he felt were the consequences of pre-hypovolemic shock, but he couldn't remember how he ended up losing blood. The only assumption he could make is that he figured got wounded during the time-travel or because he landed somewhere unsafe outside of it.
The pain of his back (that was actually coming from a wound he got from ShiHao) seemed to confirm his hypothesis.

But the real source of his different attitude comes, mostly, from how different his 'new arrival' conditions were, compared to the ones of his real arrival.
Back then, he found himself totally alone in a country he knew nothing of. He was lost and scared, but had to do everything on his own, trade for money, settle. And naturally he went through many unpleasant situations, during that time: he got scammed, robbed, threatened, mistreated by many.
In addition to that, the scary first experiences with 'Jaguar' awakened his anxiety issues and added to the pile.

Though, the main three reasons that made him feel so unhappy and unloved, were 3:
• Finding out he was just a clone of QinShi;
• Being raped by ShiHao;
• Finding out he IS the cure to the plague.
These three awarenesses shattered his whole world, destroyed his trust on people, how could he trust anyone when his own parents were like that?, and caused him all sort of complexes of not being an actual person, not having a soul and so on.

What changed now?
Well, when he woke up, he found himself somewhere totally safe. With a person knowledgeable and kind, who was taking care of him and who surely wouldn't abandon him around. Starting his 'adventure' with someone backing him surely gave him a whole different feeling than starting all alone.

After spending some days with Christophei, and getting to trust her quite easily, he decided to tell her the truth about his 'arrival', the future, the plague and such. At the mention of that, she promptly told him that the plague, in their time, had just been eradicated as the source of it had been destroyed.
That information too changed his whole view on everything. Not just it allows him to feel free and without the burden of finding a cure or a solution to it, it also gives him the convinction that maybe his eomeoni knew of that circumstance and sent him to this specific time to save him from the potential destruction of their future, not to carry out some terrible mission.

The first days he cried a lot, but also slept a lot due to being very weakened from the blood loss (body of an adult produces around half litre of blood per week), but he also recovered fast: it's quite better to mourn the people one loved with affection than with doubt, disappointment and resentment.

Right now, he feels like the kid he is. He is confident of his skills, since he has had no reasons to doubt himself so far.
He is free and relaxed without worrying about himself or the whole.furure or their world. No wonder he can't have the same attitude of the 'real' LaNi.