Is it considered a lie to tell someone that a missed prayer being made up is the Duha prayer, out of fear of revealing the secret of making up missed prayers?

The questioner's desire to conceal herself is a good thing, and she can use allusive speech (ma'arid) to avoid lying. If she is asked what she is praying, she can answer that she is "praying rak'ahs for Allah" or "a prayer to draw closer to Allah," while intending to make up missed prayers. The questioner will understand that she is praying voluntary prayers. As for her saying that she is praying the Duha prayer, that is a lie that must be abandoned.