As for Luke's motive, it's been suggested they had a falling out at school that day. An eye witness told police she saw them outside a local chinese at lunchtime smoking a joint, and they were sitting not facing each other or talking to each other. 'as if they had just been arguing'. Police tried to link this argument to a girl Luke met on holiday who he had been in contact with while seeing Jodi. The fact Lukes DNA wasnt on Jodis body also backs the suggestion they were on bad terms that day, ie no hugging or contact. Prosecution suggest their was a meeting arranged between Luke and Jodi behind the V cut in the wall, (the half way mark basically for both of them) where they were going to have it out about this other girl. This is purely speculation by me: Jodi's mobile phone was broken around the time of the murder, so her using Luke's mobile could be one possibility for her finding out about the other girl. She and Luke had been texting regularly.
Im not sure where you got any of this as all of it looks to me as you have read a little and then assumed too much!
They were nevers seen outside a local take away, I think you read about an area they called the chinese garden and came up with a load of rubbish. This area was a secluded area out with the school where pupils went, Jodi and Lukes friends went there to smoke dope and they were in the company of another boy(atleast one) who stated they were normal.
Jodi confided in friends about much of what was personal to her including things like self harming and according to police files also about other relationships, so why after lunchtime when Jodi had not been with Luke in class or shared a bus home with him didn't she confide in her friends about what you state?Why would they have it out in a secluded spot?
If any of what you say could ever be verified this must occur 1000's of time throughout the world on a daily basis and very rarely leads to a brutal murder, I will put my neck on the line here and say never between 14 years old kids.
Luke would have had to have thought ok I have been rumbled here and Jodi wants to meet so I better take this bloody big knife with me to shut her up! I better tell my mother to cover for me and help me get rid of all DNA from the crime scene. I better not be seen by anyone on the way even although independant witnesses see 2 people who were on a bike and that bike propped next to wall at the very scene and time and them even to this day never saying where they were but they also don't see Luke.
I see why you think this might mean that none of Jodi's DNA was found on Luke but there is a far more plausible reason for that anyway.
I have read loads of rubbished spouted about this case but thats close to the craziest so far, I would love to read your story on how he managed it with no DNA or the slightest amount of Jodi's blood on him, no murder weapon ever found! him doing it in the timescale required.