If they have a warrant without restriction, yes they can.
It is worth noting the phrase "military lodge" can have different connotations. I would imagine you refer to traveling warranted lodges comprising members of the military traveling with a certain unit. Here, Military Lodges are simply those who have a military focus. We have several; Army Lodge, Victorian Naval and Military, & United Service. Several have decided to surrender their warrants in recent years and they included Commando Memorial Lodge and also Vietnam Veterans Memorial Lodge , the first being a post WW2 lodge, the second being one where many members were Vietnam Vets and decided not to operate their lodge anymore.