If phplist does not exactly do what you are looking for, you could consider any of the following applications, that do similar things. Mailman
Mailman is probably the most popular open source mailing list application. It has a web based admin interface and it has a lot of useful features. It is written in Python. Unlike phplist, mailman allows posting via email and posting from users to users, which may come in handy in many situations. It's worth checking out if this is what you are looking for.
Dada Mail is very similar to phplist, but it is written in Perl instead of PHP. The list of features is a bit different from phplist and the way of doing things as well, but it can be a good alternative to phplist. It all depends on what you are looking for and what you want to achieve.
Majordomo is the mother of all mailinglists, and it was around before you were born (or at least it feels that way). It's written in perl, and requires quite a bit of system access to your server to be installed. It's listed here to give it credits it deserves, but there are probably many better mailinglist applications now.
Ezmlm is the mailinglist software that accompanies Qmail. It is very powerful, but again, you will need quite some system access to the server running it in order to install it. This system allows you to discuss with others via email.