When Lucy shades her eyes with her hand, she is genuinely interested in the Flight of the pigeons, but she has not let go of her domestic routine - her hand still holds her sewing. This story is dramatic. A lot of it is in the form of conversation. While Lucy is calm and reasonable, the old man and Alice quarrel like children. There are also many references to people's bodies - to eyes, legs and hair.
Comparisons are very important here.
Many of them are to natural things. Later Alice and Steven tumble like puppies - they are not yet enjoying adult pleasure but their play is a preparation for what comes later. This story is very obviously one where symbolism is important to our understanding. Alice is clearly likened to the favourite pigeon. The old man can keep the bird in, where he cannot control Alice.