HP Printer in Lx 3 printing broken

I have neither a HP printer not any remaining Lx3 boxes (please check 4), but some of this is odd:

“Failed to create /var/spool/cups/tmp/.hplip”

Probably a permissions issue. Does the directory /var/spool/cups/tmp exist? (The cups package is supposed to contain it, and it’s supposed to be owned by user root, group lp, permissions 1770)

“/dev/lp: Permission denied”

That’s trying to create a file called lp in /dev – you don’t have permissions to do that.
what you probably meant is cat print_test_page_output.txt >/dev/lp0 (but isn’t that for ancient parallel port printers only? Probably not going to work either way. This is a usb printer, right?)

The strangest things are the “Unsupported document-format” errors - application/postscript should be handled by /usr/share/cups/mime/mime.convs, text/plain should be handled by /usr/share/cups/mime/cupsfilters.convs.
Are those files there and readable?
Is the cups-filters package installed?