When you concoct a soup, or concoct a plan, or concoct a lie or a story, you make it, create it, or invent it, usually out of many parts that you put together.
The word "concoct" has Latin bits that literally mean "to cook together." If you're creative in the kitchen, then you're always concocting new recipes: creating them by combining different, interesting ingredients in fun new ways.
If you concoct a story or an excuse, you're inventing it: making it up, and trying to pass it off as true.
For example, here's Lane again, concocting an excuse to avoid paying the newspaper boy. "The problem here is... my little brother, this morning got his arm caught in the microwave and um, my grandmother... freaked out and hijacked a school bus full of penguins, so it's kind of a family crisis, so, come back later? Great!"