The phrase "lay claim to something" can be expressed in various ways to convey the same meaning. Synonyms for this phrase include "assert ownership," "claim possession," "lay hold of," "declare as one's own," "take possession of," "occupy," "seize," "annex," and "garner control of." These synonyms can be used in a legal context or in everyday situations when claiming something that belongs to you or someone else. It is important to choose the most appropriate synonym in every situation to avoid misunderstandings and to communicate effectively.