"Last of all, he said, 'Lucy, Eve's Daughter' and Lucy came forwards. He gave her a little bottle of what looked like glass (but people said afterward that it was made of diamond) and a small dagger. 'In this bottle,' he said, 'there is a cordial made of the juice of one of the fire-flowers that grow in the mountains of the sun. If you or any of your friends is hurt, a few drops of this will restore them. And the dagger is to defend yourself at great need. For you also are not to be in the battle.'
'Why, sir?' said Lucy. 'I think-I don't know-but I think I could be brave enough.'
'That is not the point,' he said. 'But battles are ugly when women fight.'" (Lion, Witch, Wardrobe, 108-109)
Valiance: brave, courageous and faithful
The cordial and dagger show her Valiance. The cordial shows her bravery because she is a healer. Healers routinely have to show more bravery then most people, because they have to face injuries and illnesses that ordinary people do not have to face. Sometimes, it seems like Lucy had to be even braver then the two Kings, because they just had to fight the battles-she had to deal with the aftermath.
The dagger also shows her Valiance. It shows her bravery and courage because she didn't have to fight in any battles. She could have stayed at Cair Paravel with Susan, and let Peter and Edmund take care of the wars, but she didn't. She came to their aid on several occasions, like when she led the Narnian archers who were fighting Rabadash. Father Christmas told her that battles were ugly when women fought, but she felt comfortable about making the decision about when to fight when she grew older.
The cordial and dagger show her Valiance.