I can see this information when I initially connect, but is there a command I can run to see an updated list?
in the whichever channel you want a list of users for. This is the IRC command to do what you want.
You can issue the command
who #channel, which will list the users currently in the named channel.
Exactly how you'd do it and exactly how the output is displayed depends on the client; I'm not familiar with irssi so can't really comment on that.
For other IRC commands, see for example technerd.net's summary of IRC commands. Note that many of those may very well be server-dependent.