Can't help with the book, I'm afraid, but it was published just when flower names for girls were all the rage.
The nerine is a bulb of the same family as the amaryllis. It's got medium-sized, graceful flowers, shaped like an amaryllis flower but smaller and less bulky; there's a few of them on each stem and they droop down a bit. The best-known ones are a soft red, but you also get orange and pink. They are really beautiful! If you can't find the book, and even if you can, why not try to buy her a nerine bulb so you can watch it flower together?
Nerines are South African plants, but there's one type that's known as the Guernsey Lily because a ship bringing plants to England was wrecked in the Channel Islands and the bulbs were washed up on Guernsey. People grew them and confused the scientists for a while, but the truth emerged! Your plant dealer might know them as Guernsey lilies, though. Nerine means From the Sea, I think; they are native to the coastal regions of South Africa, but then there's also the sea around Guernsey as a possible reason for the name.
Hope that's helped. Sorry about the book, but what a marvellous choice of a name! Just think, you and your aunt could have been Olive or Pansy ... instead of which, you've really got a winner.