You may have seen this from me before, but the loss of a dog is the loss of a family member. Weirdly (but that fits me) I always think about the end of Watership Down when I hear of a friend losing a dog. If you don't remember, Hazel is the hero who guides his rabbit friends through their adventures to establish their new home. Hazel had reached a very old age and this is how it ends:
It seemed to Hazel that he would not be needing his body any more, so he left it lying on the edge of the ditch, but stopped for a moment to watch his rabbits and to try to get used to the extraordinary feeling that strength and speed were flowing inexhaustibly out of him into their sleek young bodies and healthy senses.
"You needn't worry about them," said his companion. "They'll be all right -- and thousands like them. If you'll come along, I'll show you what I mean."
He reached the top of the bank in a single, powerful leap. Hazel followed; and together they slipped away, running easily down through the wood, where the first primroses were beginning to bloom."
I imagine Lucy is out sniffing some fine scent enhanced by a fresh rain, looking down on all the Utees with love, smiles, and tail wags, knowing that she left you better than she found you.