From version 3.6.0 the PHP system requirement is PHP version 7.0 and higher.
It is likely that phpList will continue to work on older versions of PHP, but the phpList core team is no longer testing that, as it has been found to be too time consuming. If you would like to ensure that phpList continues to work on older versions, you are welcome to help out with testing that, and sending pull requests for changes required for this.
It is unlikely phpList will work with PHP older than 5.3.3. However, we strongly advice to update your systems to use PHP7.3 or up, as those are the versions supported (January 2021)
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