In the first chapter (page 7) of William Golding's allegorical novel "Lord of the Flies" (1954) we find: "He came forward, searching out safe lodgments for his feet, and then looked up through thick spectacles." Later we also find: "Roger found a lodgment for his point and began to push till he was leaning with his whole weight."
A lodgement is a place of rest or deposit. A shelter can also be termed as a lodging place.
Every time we take a step, we lodge our feet on the ground. In this context, "lodgement" simply means a place where the boy could safely put his feet without stumbling or tripping. This conveys an impression of the boy's vulnerability and awkwardness.