He offers over the cup of water he hasn't yet touched, letting her have it. Once he has his hands free, sword left by his seat, he rises to bow to her respectfully.

"Lady Minazuki. Gusu Lan clan Sect Leader, Lan Xichen. Zewu-jun."

Don't worry, he sits down shortly after; he doesn't intend to make a spectacle, only to be properly polite. Xichen swats at his skirts as he sinks back into his seat, finding his bowl of soup again.