↑Oxford English Dictionary lodgement, lodgment "3. The action of establishing oneself or making good a position on an enemy's ground, or obtaining a foothold; hence, a stable position gained, a foothold. Chiefly in phr. to make or find a lodgement."
↑United States Department of the Navy -- Naval Historical Center 805 Kidder Breese SE -- Washington Navy Yard Washington DC 20374-5060 Chapter X: The build-up for the Battle of France; Part 1: The post-NEPTUNE naval task "The army still had a desperate battle before them before they would consolidate possession of their bridgehead in the lodgement area."