In addition to the other good ideas here, there is a lot of expertise about schools generally, and the lottery in particular, on the cpsparents email list. You can get some info at https://cpsparents.groups.io/g/main or just subscribe via email to main+subscribe@cpsparents.groups.io. It's been quieter lately but this is just the kind of question where the wide-ranging membership there will likely have useful comments, both about the lottery and specific schools.