The phrase 'give the lowdown' refers to providing information or details about a topic. Antonyms for this phrase would be to keep secrets or withhold information. Other antonyms could include to conceal knowledge, remain tight-lipped, or refuse to disclose facts. Instead of giving the lowdown, someone could be evasive, deceptive, or unforthcoming. Antonyms for this phrase may also include providing inaccurate or false information, misinforming, or even gossipping. Whatever the antonym may be, it directly opposes the idea of sharing information or being transparent about a situation.