Be sure to test, but if you run lat-users with the new password you should get a polite message saying 'updating existing entry' or 'updating existing values'.
In either case, you can run lat-dump -d, then edit the <servername>.Users file that gets created, replace all the passwords, then use lat-users to "restore" the dump file with the new passwords.
After running lat-dump you will have a new file 'lat-restore' that will show you the proper syntax for reloading the <servername>.Users file.
Don't run the whole lat-restore - that restores all of the dumped data (users, ibays, hosts, quotas, domains, groups, procmail rules, pseudonyms, and pptp permissions)