You can lie to spare embarrassment.
The Pasuk in the Torah is talking about Eidus. When the Gemara talks about not meaning a promise you are making to someone we Darshen Hin Tzedek, that your yes should mean yes and no should really mean no.
Simple conversational lying is a bad Mida, and is included in the Pasuk in a general sense. On this the Gemara says that Kat Shakranim are not Mekabel Pnei Hashechina.
When a nosy person is intrusively asking you something personal, you do not have to answer. It is best to avoid or skirt the issue if possible, or try to give misleading or hollow answers. When left with no choice, having said something that isn’t true, when the person doesn’t deserve the truth, does not place you in the Kat Shakranim.