The original mail.local program was executed like this:

mail.local -d user

Here, mail.local is not running LMTP (the -l command-line switch is absent). Instead, it is running just like the old /bin/mail program. It reads from its standard input and writes to the user's mailbox.

The modern mail.local program can be run like this:

mail.local user

This invocation has the same effect as the first one earlier. Thus, the use of -d is optional and can be included or omitted with no change in effect.