Before starting an exercise program, the individual should get confirmation from his/her surgeon indicating readiness to participate in a program. Additionally, the patient should also contact her physical therapist before beginning a new exercise program to discuss precautions and appropriate expectations. Ideally, the individual will continue with a progressive resistive exercise program designed specifically for her by her physical therapist.
Once the individual has been cleared by the surgeon and physical therapist, she should be encouraged to participate in exercise programs that enhance fitness and health maintenance. Specific to your question, there are a number of research studies that cite the use of at least partial (1/4) lunges and squats as part of an effective post total-knee arthroplasty rehabilitation program. The patient that you described should work within her pain free zone and be aware that she may still have some weakness in her quadriceps, so she should start easy. If you have questions, contact her physical therapist for advisement.