Stephen Anderton's book is titled Christopher Lloyd: His Life at Great Dixter.
Garrett and garden writer Anna Pavord will launch a rival book, Reflections on Christopher Lloyd in October, with contributions from Lady Mary Keen and Rosemary Alexander.
The museum is hosting a retrospective — Christopher Lloyd: A Life at Great Dixter — from 1 April.
Keen and Garrett have been critical of the personal nature of Anderton's book, which describes Lloyd's private life. Anderton, who was not available for comment, makes many references in the book to Lloyd's "passion for youthful gardeners".
Garrett, now also chief executive at the East Sussex garden, said of Lloyd, who died in 2006: "He was a real sweetheart - a fantastic, kind man with a big heart. I don't want him portrayed as old curmudgeon.
"He was a great human being. He certainly was not hunting for young men. What drove him was a passion for plants, for interesting people and for a good social life.
"The private stuff is not a problem but rather that the book makes him seem predatory and he wasn't. The big issue is whether or not Stephen has been tactless."