You know, it's entirely possible that Lina's mistaken Allura for someone who belongs here. Not Arthur himself, for obvious reasons, but given the literal princess gown she's wearing? And her jewelry, including what appears to be a literal crown? Everything about her screams 'royalty'. It's reasonable to assume she would call this home, too.

But in fact, nothing could be further from the truth. In fact, that's part of the reason why she took notice of Lina and approached her. Which is why she responds...

"Do you? Perhaps you can help me out, then. I took a wrong turn somewhere, and... I think I might be lost."