The phrase "gave the lie to" means to prove something false or to contradict a previous statement. Synonyms for this phrase include "disproved," "debunked," "refuted," "denied," "contradicted," and "exposed as false." Other similar phrases to convey the same meaning include "put the lie to," "showed to be false," and "called into question." These words and phrases are often used in journalism, politics, and legal settings when discussing the veracity of a claim or statement. It's important to have a range of synonyms to convey the appropriate level of emphasis and to avoid redundancy in writing and speaking.