phpList 3.4.0 and latter feature the new REST API. PHP 7 is required to use the API. The phpList3 module requirements are the same on those versions too.
Some module dependencies are not obligatory. Some of phpList's functionality will be hidden if certain functions are not available on your system. For full phpList functionality all the above modules are required.
phpList plugins have independent system requirements and sometimes use additional PHP features and modules. Please check the documentation of those plugins for requirements before upgrading them.
If you use Puppet to manage the software on your server, there is a puppet module to automatically install phplist at https://github.com/Ecetera/ecetera-phplist.git