Imparting second meanings to the Psalms was common even in Jesus’ day. Learned Jews would have seen the references to the Messiah in the OT, but would not, mostly at least, have agreed that Jesus was the Messiah.
Lewis talks about the Christmas Psalms and how they capture the Nativity and the purpose behind the Incarnation better than Christmas Carols and even in a different way than the gospels.
He ends with a comment on the one day is like a thousand years (and vice versa).