FWIW I would believe the later time. My involvement in this case came from a post on nextdoor. I generally get home from dropping kiddos off at ~8:55. As soon as I got home I saw I had notices on a nextdoor post I had been following about people letting off loud fireworks. It turned out to be Charles' murder. No more than 10 minutes after I checked the thread another poster said they had just driven by the street where Charles was shot and reported a lot of police presence. That's when everyone surmised it was gunshots and not fireworks they heard.
Well if Lori is truthful about the school being 15 minutes away, she had to have left by 8:18am, minimum. That doesn't include the time for getting out and taking JJ inside to his teachers, or time to buy and eat breakfast on the way.
I'm more inclined to think 8am is closer, because Tylee said she woke at 7:50am, and I think she was still in her pjs when they came back, so I think she's telling the truth there. There's a limit to how long they could string out the yelling and commotion with JJ outside alone in the car and Lori thinking he might come back in.
Also Alex's replies seemed nervous when he was asked what time he shot. He tried to fudge over that by saying he took time to compose himself before calling 911.
One last reason seems to be that Lori would want JJ to arrive on time for school, so that she could leave him with minimum of fuss. I bet she never said a word about any of it to Tylee in the car before she'd dropped off JJ, because she wouldn't want him repeating anything at school.