No. It is not possible to drive BMH from LXM05. The LXM05 needs a temperature sensor and the BMH has no sensor.
LXM05 cannot drive BMH. Only BRH, USH, BSH and SER can be driven by LXM05.
LXM05 cannot drive BMH. Only BRH, USH, BSH and SER can be driven by LXM05.