The simple past tense of lie is “lay.” So the past tense of the phrasal verb lie down is lay down (e.g., “Little Timmy came in and lay down on the sofa”).
“Lay” is also the infinitive form of another verb meaning “put down gently.” However, while “lie” (and its past tense form “lay”) is never accompanied by a direct object, “lay” (meaning “put down”) is transitive, so it is always accompanied by a direct object.
The simple past tense of the phrasal verb  “lay down,” meaning “put down” or “enforce,” is “laid down” (e.g., “Asmita laid down the rules for the camp”) because “laid” is the past tense of lay.
The QuillBot Grammar Checker can help ensure you’re using phrasal verbs like “lie down” correctly.