lodge

English lodge comes from Middle English logge, from Old French loge ("an arbour, a covered walk-way"), which traces back through Frankish *laubijā to Proto-Germanic *laubą, related to the idea of leaves and foliage.

What began as a leaf-covered shelter or walkway in Old French became, in Middle English, a general word for a small dwelling or hut, the sense of covered, sheltering structure carrying through into modern English.

It's a doublet of loggia and lobby, both descending from the same Frankish and Old French roots for a covered gallery or walkway.