Your sister has the gift of alliteration, and she seems to think that you have a skill, too: that of lying. Prevarication is deviation from the truth; prevaricate
softens the bluntness of lie
by implying quibbling or confusing the issue.
In Thomas Hardy's Jude the Obscure, Jude and Sue are an unmarried couple seeking a place to live:
When [Jude] was gone the landlady came up to talk a little with Sue, and gather something of the circumstances of the family she had taken in. Sue had not the art of prevarication, and, after admitting several facts as to their late difficulties and wanderings, she was startled by the landlady saying suddenly:
"Are you really a married woman?"