On the willows there, we hung up our lyres

Lan Wangji is not ignoring them. He is perfectly aware of their presence. But because Galahad is speaking so quietly, he opts to leave them be, in the event that they are sharing something private, for only the two of them. He finishes copying his note about the existence of this piece of evidence. He will keep one and give the other to Claudius as soon as possible.