When I try to scp a file to a router on its console port, it says: "lost connection"
Is it not possible to share a file with the router on console port? If not, why?
SCP requires SSH which requires a working TCP/IP connection which doesn't exist over a console connection. Unless the Juniper supports terminal-style file transmission like XMODEM or ZMODEM (which I don't think), you're out of luck.
So, SCP will use TCP/IP to transfer that file, but Serial does not work that way. Now, if using two linux servers (for example) there are some ways of doing this like piping the output to devTTY for example or installing some terminal software to handle this on either side.
But, JunOS running on your Juniper router is a locked down platform which certainly does not allow you to install some new terminal software/drivers to accommodate this.
Think outside the box here, can you not pass a command over console to download a configuration from an FTP directory or WWW?