Group project really drives me crazy sometimes..

(This conflict i had just encountered one or two days ago)
I had just finished a presentation who i did with three other members. it worth 30% because it includes lots of elements such as research, design logos, business cards, magazine advertisement, since it's a CCT course.

Here's my story, my group has four people, so I'll just named them by I ( represents Me), J , K , L when my group was trying to work on the project one night at the library, J couldn't come because he had work, but he already did the most he could and sent his part to us. So basically, we have only three people to work, but it sort of equals to two people's outputs only, because L wasn't contributing at all. K and I were working all the way through, and when we asks L to simply "START" brainstorming ideas for the magazine Ad, she rejects and tell us that "I'm not good at design, i want to work on some other things." we were shocked by that reply, because she's taking double majors on econ and cct, I'm not saying everyone would be GOOD at designing, we are not perfect, so that is why we want to take these courses to strengthen our expertise and help out each other. But without even trying, she already puts up a "give up" sign, we definitely felt very frustrated. So K and I didn't want to force her, so we just asked what would she want to do, so she picked to work on a simple task by writing down our work schedules of time and locations we met that's supposed to take up just less than half an hour, but took her almost two days to send it to us, but it was way passed the deadline we set up for each task. We don't want to push her too far, but it is really time-consuming and annoying to keep telling someone to complete the task within a "reasonable" time period. K and I were working on all the "design process" because L didn't even want to try and B already did everything he was responsible to. Another frustrating point is L kept
complaining the minor imperfections of whatever K and me had in our work, we accept more suggestions because we want to improve our design, but when L doesn't do what she was supposed to do and pushed the ball to us, she should understand our limits. And L was so good at pointing out the negative things and firing complaints at us, so we were trying to ask her if she wants to work on the Ad since she seems to be knowing what would be the RIGHT thing to do. But she rejects again, and going through the materials i learnt from MGM300, i believe that this person, L, rejects to complete certain tasks we assign to her, is because she is afraid of failures or the negative feedbacks from others toward her work. She is being very conservative and curious on lots of things, because she believes that doing less work would lead to less mistakes being made. But we already explained to her that even a simple shape can be a design, and it doesn't really have to look super amazing to be called master piece. And since we are in the same group, we should contribute equally and hand in work with "QUALITY" as well. At the end, K and I did almost 70% of the whole project. is that fair? but since we knew L for quite a long time, so it was really hard to tell on her. So i realize that working in group with people you know really well might be a troublesome barrier to getting work done effectively and efficiently with fair contributions.

P.S: maybe i should really set up a table of expectations or rules that everyone in the group must follows despite the fact that how long I've known certain members for. Because it might help to increase productivity.