I think this is about the clearest article about it.
www.bbc.com/news/business-58235479
It basically comes down to funding. As a pp said, NASA had originally said they would select two companies to build a lunar lander, but due to funding cuts, they were only able to select one. (They do this so if one is rubbish, they can use the other instead.)
Jeff Bezos finds it wildly unfair that NASA chose the cheaper and potentially more reliable (and definitely more experienced) company, but is possibly rightfully angry that NASA first committed to choosing 2 companies, then moved the goalposts and only chose one (which is why he’s suing, as his company potentially lost out.)
Bezos isn’t suing about access to the moon. They need NASA “permission” (although that’s not quite the right word!) as it’s a NASA funded, NASA staffed collaboration, using NASA resources.
It’s not a case of NASA denying permission for Jeff Bezos to launch an independent mission. Blue origin bid for a NASA contract but their offer wasn’t good enough/cheap enough for what NASA needed.
Hope that makes sense? It gets a bit like a soap opera when you dig into who’s suing who for what, and who’s passive aggressively subtweeting who 