I have an old (2010ish) MacBook that needed its hard drive completely wiped.
Restoring the OS has proven extremely difficult, because the automatic Software Recovery always reports an error along the lines of "the software cannot be found" or something like that.
It was intensely hard to make a USB Install disk because the Lion installer refuses to work on machines that can't natively support Lion, and I don't have any of those anymore.
I finally did it, though, finally finally, by booting into Recovery Mode using the MacBook itself, then using the Terminal, following the directions at these links, and figuring out a couple things on my own when the directions to drag things from one place to another weren't possible:
https://docshare.tips/make-a-bootable-usb-drive-os-x-108-mountain-lion-recovery-partition_587b4cf7b6d87f19538b5166.html
--and--
https://silvae86.github.io/2020/10/15/restore-mac-dmg-only-using-terminal/
ANYWAY now that I finally have a working USB installation disk, that successfully connects to the app store, it keeps rejecting my attempts to provide an AppleID. It keeps telling me I have an incorrect password or email, and I think I figured out what's going on.
When I try to sign in to the App Store via the Lion Installer, I get sent a message on my other computers about two-factor authentication. I suspect the App Store is just following its normal protocol requiring two-factor authentication. Problem is, Lion has no ability to handle two-factor authentication. I get sent a code, but there's no way to enter it. I think Lion interprets this as a failed password/email combo.
I suspect the only thing left for me to do is find an actual Lion install disk, somewhere (they don't seem to be easy to find), so that I can install it without any attempt by the MacBook to contact the App Store.
But I'm posting here in case there are any other ideas, because for the life of me I'm at wits' end.