The Quick Red Fox (1964) is the fourth novel in the Travis McGee series by John D. MacDonald.
In it, McGee is hired to aid a fictitious Hollywood star named Lysa Dean who is being blackmailed with revealing photographs.
Four languid days and all the booze they could drink...Ten playful people swinging wild and free, getting drunk, getting bored, swapping partners in the warmth of sun on naked bodies, miles from civilization.
Except there was another woman involved, a lovely, longing, tender woman whose life was slowly draining away into disaster..." The title phrase, "The Quick Red Fox" is mentioned at two places in the book referred to Lysa Dean, the movie star that Travis McGee is employed by.
The character "Lysa Dean" makes an appearance in Free Fall in Crimson to help Travis solve another case.