At what systolic blood pressure do you recommend a person 73 years old who does not show any thickening of the heart walll to go on medication?

Depends. In general terms, people with a systolic blood pressure consistently above 140mmhg and/or a diastolic pressure over 85mmhg need treatment to lower their blood pressure. Even if the patient shows no signs of atherosclerosis, I am sure there is some present. I just would go slow on lowering the pressure so the patient does not have se of the medication. Don't forget a dash diet and exercise!
140. A healthy 73 year-old likely has another 20+ good years to go. Even mild hypertension can damage the heart. You may need only a simple medication like a diuretic. Follow your doctor's advice. Wish you many years of good health!
Above 140mmHg. Assuming the patient is in otherwise good health and can tolerate treatment. The patient would benefit from treating levels consistently above 140 mmhg.