MAKE UP (something) （～を）でっち上げる

To make up an excuse, a story, etc., is to purposely say something that's not true.
言い訳や話などについて make up と言うと、故意に真実ではないことを言う、つまり、でっち上げる、という意味です。

MAKE UP (something)

Is that a true story, or did you just make that up?
That student I was telling you about didn't turn in the assignment again today. He made up some excuse about the dog eating it.
(reading a magazine)
a: It says here that a UFO landed near the Pentagon last week and brought back Amelia Earhart - and she hasn't aged a day!
b: You don't really believe that, do you? They just make those stories up.

英会話レッスン Hey, we don't make this stuff up!