Is my denial of my sister's cursing a man, without mentioning its details, considered a lie? And what is permissible lying, and how does it align with covering up for others?

Concealment [of truth] that is permissible through equivocation (tawriya) is allowed, unless it leads to nullifying a right, validating a falsehood, or similar outcomes. If you are asked, "Did your sister hit a man?" your answer "No" is considered truthful if you were present and your sister did not hit the man, or you were unaware that she hit him. However, if you were not present for the incident, the default is to say, "I don't know," because she might have actually hit him.