Christine Lagarde’s nomination to be the next president of the European Central Bank (ECB) to replace Mario Draghi has sparked a divergence of views on how effective she would be and where she might lead the bank. Few doubt her talents or that she will sail into the office easily. Instead, key issues include whether the straitjacket of low-to-negative interest rates prevailing in the European Union could ever offer Lagarde much running room.

Lagarde recently resigned as managing director of the International Monetary Fund (IMF), where she was the first woman to hold the position, in order to advance her ECB nomination, where she is the first woman picked to run it.…