More importantly, Osric entered the Central Tower using the same method as Lin Li and the rest despite being a disciple of the Immortal King. He, too, barged into the Seven-Realm Spiral of the Orderly Maze. He could tell from Osric's note that the latter seemed to be looking for something important, but ended up venting his anger and destroying the Immortal King's laboratory. That was not how a disciple ought to show respect to his teacher.
Lin Li could not guess what Osric was looking for, but it was unlikely that it would be the magical crystal that controlled the Sky Castle. The sixth floor of the Central Tower was completely sealed by the Immortal King using the space trap, so Osric probably wouldn't have been able to enter, either. However, Osric should have known that the magical crystal was right there. If his goal was the magical crystal, the words he wrote on that note should be his complaints, and not a clue about where the Immortal King had hidden the item.