1. To make up an idea or story which is not true, often for dishonest reasons. English = make up, invent, concoct, contrive.
2. To think imaginatively about something for creative pleasure or because you would like it to happen even though it is unlikely to happen. English = fantasise, make believe.
3. To make up a story, based on something that actually happened, but with some details changed or added. English = fictionalise.
4. To say something in a play or speech which has not been planned or prepared beforehand; to give an answer when you do not know if it is correct. English = ad lib; guess.