Lodges are an aggrupation of like minded packs of Nahuals that have sworn an oath that is generally set in place with the help of an Xilotēki or a Icon.
While there are Lodges that could be considered antagonistic or heretical, in truth there are no good or bad lodges. Lodges just exist and each one of them has a particular set of goals they want to achieved, so one Lodge might be at odds with another lodge of the same region for any kind of reason not only because it is formed by Estranged Children.
Lodges are regional and while they can sometimes expand their influence across an entire country, they generally do not expand beyond the provincial or city level of a country due to lack resources and management. Given this limited scope there are not worldwide lodges. Plus a lodge in Alaska is generally not aware of the existence of another lodge in Turkey that may have like minded ideals, and even if they did they would not care since for them that lodge is that lodge and their lodge is their lodge.
While Lodges are generally conformed by only one brood of Nahual, there have been cases of mixed Lodges that include other kind of nahuals apart from the founding type and even included other supernaturals as well.