When Lloyd met Antony Tudor in one of Rambert's classes in 1930, she was immediately drawn to him, and he to her. She, along with Hugh Laing, became one of his muses, inspiring him to create numerous works with roles focusing on her special qualities. "Not only was she very pretty, with beautifully curved feet, but she also danced with a rich, natural expressiveness that fed the psychological realism with which Tudor was experimenting." Of the numerous Tudor works in which she danced leading roles, none has been more enduring than "Jardin aux Lilas" ("Lilac Garden"), premiered in 1936. Lloyd's portrayal of Caroline, who gives up Her Lover (Laing) for The Man She Must Marry (Tudor), was "a beautifully modulated exposition of the simmering passions and dutiful restraint characteristic of Edwardian life." This was followed in 1937 by another Tudor masterpiece, "Dark Elegies", set to Mahler's song cycle "Kindertotenlieder" ("Songs on the Death of Children"), in which she and Tudor danced a tender, sorrowful "pas de deux" to the second song. She also made successful appearances in the classical repertory, dancing Aurora in Rambert's version of "Aurora's Wedding", the Prelude in "Les Sylphides", and Odette in a one-act version of "Swan Lake". Having danced decorous roles in Ashton's "The Lady of Shallot" and Howard's "Cinderella", she appeared in a more boisterous role as the can-can dancer La Goulue in "Bar aux Folies-Bergères" by Ninette de Valois. One reviewer of the roles in Lloyd's repertory described her as having "a noble serenity and a deep expressiveness allied to sparkling gifts of comedy."