When does your school start back? My senior’s first day of school is this Thursday. She doesn’t have any LORs yet either. I think it was tricky this year with so much online. She did not get a lot of support from the school for college prep last year and pretty much none over the summer, but she does have an appointment with the guidance counselor when school starts up so hopefully your school will start scheduling those soon too. As I understand it there is usually no advantage to completing your application in Aug/Sep/Oct, but Nov is the ED deadline for many schools, so as long as they get those LORs by then they should be good.
You might like to join the thread here: Parents of the HS Class of 2022