LogonBox does not currently support authenticated proxy servers for outbound access.
However, if you want to update the service via such a proxy, this article shows how this can be achieved from a shell.
From a shell or SSH session do:
Put 2 lines in like this, adjusting to your needs:
e.g Acquire::http::Proxy "http://proxy:firstname.lastname@example.org:3128";
Save the file with CTRL-X, Y
then try: apt update
This should then make the connection via the proxy and authenticate to that server.