I'm not a doctor, but my understanding is that lower blood pressure can indeed lead to a higher heart rate under certain circumstances. For instance, people taking minoxidil for hair loss can experience lower blood pressure, which leads to higher heart rates and increased left ventricle thickness as a side effect.

My suspicion is that this happens because the heart is trying to maintain a constant oxygen supply to the muscles. However, if blood pressure is lowered by improving factors like arterial flexibility, stroke volume (amount of blood per heartbeat), muscle oxygen efficiency, or oxygen content in the blood, the heart wouldn't need to pump faster.