"Make something up" ~compensate for something lost, missed, or deficient.

The most common meaning is to invent something, such as a story, or tell a lie 'She wanted to get him in trouble so she made up a story about him stealing her car'. I didn't have a recipe, so I made something up'. It can also be to compensate - I didn't do enough hours at work this week, so I had to make it up by working late on friday.

'make somthing up' is to make a story .excuse or anything that you can use as a reason or as an answer even though it may not be correct or true. Eg . Im afriad my mum will scold me for being late so i just made something up as an excuse