How fast can a DVT in the calf area travel to the lung if broken off?

Within seconds. A clot can travel in the large veins of the legs up the vena cava and into the right heart and out to the lungs in a matter of seconds.
2 seconds. Once a clot is free in the vein, it will travel immediately to the lung.
DVT. Can be very rapid. It is not rare for there to be clot in the lung already at the time DVT is diagnosed. Anticoagulation reduces the chance that it will happen or recur.