I think you’ve gotten some good advice already about establishing a good cardio base for your deconditioned client. I’d just like to add that she can get some cardio benefit from the strength training itself. If you are working with your client on strength training, you will gradually notice her ability to move from one exercise to the next with better endurance (assuming her weights are appropriately heavy enough to challenge her). You could try alternating upper and lower body exercises to keep the heart rate up–appropriate for her level–and monitor her Rate of Perceived Exertion. As her stamina progresses, you could try adding in some low intensity intervals or even adding some upper/lower body combo movements as intervals.
I would go slow and focus on proper form and RPE–then take it from there.