It either means to fabricate/invent/lie about something or it means to do something that you should have done previously. Both have to do with 'missing' something, in the case of lying, it's replacing an inconvenient truth with a more beneficial detail, story, that was 'missing' from reality. First case: "I can't recall the details, and I don't want to make anything up, so I won't say anything." Here, 'to make up' would be to lie, fabricate a story, 'come up with a story,' etc. Here, it would have a negative connotation. "Inventors don't have a preexisting blueprint for their design, so they have to make it up as they go along." Here, it has a neutral or positive connotation. Second case: "Johnny missed class last week, so when he returns, he will have to make up the work he has missed.

"Make it up" and "make up" mean the same. The only difference is that "it" acts as a placeholder for the thing that is made up. "Make up" can mean "invent" or "imagine" or "improvise": "She made up the recipe as she cooked dinner. She made it up." "The singer made up the song. He made it up." (he is the one who created it) "He and she made up a design plan for their new garden. They made it up." That is one meaning. It can also mean doing something that was not done earlier. For example: "Since he had been sick on the day of the examination, he made it up by taking a re-test".