Honestly, this question comes up a lot and it's tricky because there isn't one definitive 'Lily of the Valley' book. The title is used for several different works. The one I think you're probably asking about is the French novel 'Le Lys dans la Vallée' by Honoré de Balzac. That's the most famous one. The key characters there are Félix de Vandenesse, the young man narrating the story, and Madame de Mortsauf, the married woman he's obsessively in love with. She's the 'lily'—pure, unattainable, and ultimately tragic. Her husband, the Comte de Mortsauf, is a sickly, difficult man, and their children, Madeleine and Jacques, play a role in the suffocating domestic atmosphere.
There's also Lady Arabelle Dudley, an English aristocrat who becomes Félix's mistress in Paris, representing a passionate but cynical contrast to the idealized love he feels for Madame de Mortsauf. The whole thing is a masterpiece of unrequited feeling and social constraint. If you're looking for a different 'Lily of the Valley,' like a modern romance or a mystery, you'd need to check the author because the cast would be totally different.