Carole Cook and Paul Kent were former students at the Desilu Workshop. They are playing for money to open a theatre which will become known as the Melrose Theatre in West Hollywood.
Interestingly, "The Lucy Show" (which was halfway through its third season) is not promoted or mentioned here. Ludden does, however, wish Gary luck with his radio show. This is probably "Let's Talk To Lucy," which he produced for Ball.
Lucy and Gary talk about playing a lot of golf for relaxation.