Litespeed and Plesk work in most cases without issues. However, the webmail (Roundcube and/or Horde) server might require additional tweaking when you have one of the following errors (or similar to unknown PHP methods/classes):
[11-Aug-2020 19:36:56 UTC] PHP Fatal error: Call to undefined function filter_var() in /usr/share/psa-roundcube/program/lib/Roundcube/bootstrap.php on line 49
[12-Aug-2020 09:09:12 UTC] PHP Fatal error: Call to undefined function mb_internal_encoding() in /usr/share/psa-roundcube/program/lib/Roundcube/bootstrap.php on line 86
Litespeed uses the default PHP version assigned to lsphp, which usually is PHP version 5.6. Plesk, however, requires PHP version 7.3 to run Roundcube smoothly. This is also the default PHP version for webmail defined by Plesk, but Litespeed ignores this.
By linking lsphp to the correct PHP version, you can resolve the issue.
mv /usr/local/bin/lsphp /usr/local/bin/lsphp-bk cp /opt/plesk/php/7.3/bin/lsphp /usr/local/bin/lsphp cagefsctl --force-update systemctl restart litespeed