The characters in the novel are survivors of the Great War. There is a profound lack of faith in all social structures and a growing fear of the future of mankind. This bleak fatalism prevents them from planning for the future or conceiving of anything beyond the present. Daisy exemplifies this by asking about how people plan. She lives day by day and does not value anything beyond the moment. Her daughter brings her no joy and her marriage is an empty shell. She is the epitome of the lost quality of the post war generation.
I think that part of this is going to lie in your description or definition of "the Lost Generation." A part of this is going back to Stein's definition and clearly establish that Stein uses the term to describe those who have lost the ability to believe in anything, and have succumbed to a cynical hedonism as a result.
It is here where some connection to the flappers in Fitzgerald's work can be present. Jordan Baker is a great example of someone who has forgone morality and embraced the pursuit of the self- interested life as the most important element for her. Tom Buchanan does not believe in any set of ideals unless they directly benefit he and his social standing. Daisy might be able to believe in some notion of idealism, but she surrenders it so easily for her own convenience and comfort that one wonders whether it was worthy for her to believe in it at all. In this light, one can see that the characters in Fitzgerald's work might be representatives of a "lost generation" on the basis that they represent much of what the term means in describing a shift of belief in moral structure to the pursuit of the life of self- interest.