The onAfterPublicSubmission handler is called after a public submission has been received, validated with no errors, and saved to your database. The $last_id field is the ID of that submission, which you can use for making additional changes, saving custom fields, etc. See below for an example module.

<?php
     $_LW->REGISTERED_APPS['my_app']=[
       'title'=>'My App',
       'handlers'=>['onAfterPublicSubmission'],
    ];

    class LiveWhaleApplicationMyApp {

      public function onAfterPublicSubmission($data_type, $last_id) {
      global $_LW;
      if ($data_type=='events') { // on submission of an event
        
        // if room_number or event_sponsor fields were set, save those values
        if (!empty($_LW->_POST['room_number']) || !empty($_LW->_POST['event_sponsor'])) {
          
          $custom_fields = [
            'room_number' => @$_LW->_POST['room_number'],
            'event_sponsor' => @$_LW->_POST['event_sponsor']
          ];
          $_LW->setCustomFields($data_type, $last_id, $custom_fields, []);

        }

      };
    }

   }
?>