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Hi, spoiler alert but yes.
J was the one who rescued lsy when he first awakened, as a little kid. They had uh a very special relationship after that until j had to go into that final dungeon (I forgot what it's called) and didn't come back. Lsy went through a lot when J wasn't around which they'll show in the later chapters.

did j and lsy already met before? like j saving lsy?