There are many writers who fall under this umbrella, Hemingway being one of the most prominent, but also such luminaries as F. Scott Fitzgerald (Hemingway's rival), Ezra Pound, T.S. Eliot and Dos Passos.
The term was coined by the writer Gertrude Stein and popularized by Hemingway in his novel "The Sun Also Rises." After WWI and the disillusionment that followed, many young Americans felt disaffected and distanced by their country. Quite a few moved to Europe where their rootlessness and search for purpose made Stein's moniker stick.
The "Lost Generation" typically encompasses the generation of artists born between 1883-1900.