The limited eight-week run will last for 14 previews and 29 performances .
Joining Weaver and Lithgow will be Danny Burstein, as Gordon, Mrs. Farnsworth’s writing instructor. Rounding out the cast are Kate Benson, Fernando Gambaroni and Tarajia Morrell.
Lithgow is currently acting on Broadway in The Retreat from Moscow, which will close its run on Feb. 29.
In the comedy, Mrs. Farnsworth is writing a book about an old lover, a profligate WASP from a wealthy clan who sounds suspiciously like George W. Bush.
The piece will be directed by Jim Simpson, Weaver's husband and the man who runs the Flea. Weaver and Simpson have teamed frequently of late, in such plays as The Guys.
Gurney, whose work is typically seen on the posh stages of Lincoln Center Theater and Manhattan Theatre Club, began his relationship with the gritty Tribeca theatre last year, when his O Jeruselum was produced there.
Mrs. Farnsworth adds to the increasingly political flavor the 2004 theatre season. Other timely dramas include Sixteen Wounded and Roar, both of which address the Israel-Palestine conflict, Embedded, about the Iraq war, and Ears on a Beatle, about the government tracking of John Lennon.