Lynne is already a member of a gym. We saw this earlier when she was commenting on Belinda's boob job. But looking at it again, that might just have been a keep fit class. Maybe Lynne go the taste for it and now wants to take her fitness to a new level.
What does George mean by wanting to 'build up our stamina'? Is it another insinuation that he would his love making to last a little longer than it already does? If that's the case then George should be laying off the chablis, as that might be affecting his performance. Also did George not expect to feel good after the workout. He uses the word 'but' when saying that he feels great. This is the sign of a man who hasn't done exercise for a while. Just look at how tired he got digging the allotment. Lynne was right that they should join a gym; George is on a one way ticket to a stroke unless he gets that blood pressure down. Being the town's topmost property solicitor is a stressful job.
Finally, once again Lynne does one of her trademark agonising pauses. George says he feels great in the middle of their workout, but Lynne doesn't respond to that until they are in the car driving home. In the meantime, George has been coughing and spluttering like an asthmatic tortoise. During that time she must have noticed that George was suffering from his first proper exercise in 10 years. She'll need to tell George not to give up though as his stamina will increase after regular visits to the gym.