I would asume it would be either a quick release on the side of the saddle or a pintle mount near the saddle horn, and the gun was fired by a standing Askari. Also, contrary to what some may think, mules are pretty calm animals, especially compared to horses. If the mule had been trained around Lewis Guns in action and had something like cotton stuffed in his ears, it's quite possible that he wouldn't kick around.
Now if they pulled some random mule from the pack train and all of a sudden fired off a burst from its back, however...