Hi Joe. As a tournament tennis player myself I fully support the notion of tennis athletes performing resistance training to help their tennis game and to help stay injury free. I’m not sure from your question what exactly your client is doing to get out of breath from lifting so you will need to elaborate on what exactly you are talking about (e.g. what exercises make him out of breath; how quickly does he recover; does he have any diagnosed respiratory issues etc.). Thanks.
The answers given are excellent. Playing viorous tennis is a different biochemistry than strength training, especially if the strength training is done at high resistance, low reps to temporary failure.
I agree with LaRue that how quickly your client recovers normal ventilation is quite important.