The following will add the class 'hello' to the li tag. I used a view with machine name 'dates' and a display name of 'page'. The time field is the node created time. You can just install Devel and uncomment the dpm($vars) statement to get what you need. I also left the conditional logic up to you.

Put this in your theme's template.php file:

function MYTHEME_preprocess_views_view_list(&$vars) {
  if ($vars['view']->name == 'dates' && $vars['view']->current_display == "page") {
    // dpm($vars); //uncomment to see variables
    foreach($vars['view']->result as $key => $value){
      $timestamp = $value->node_created;
      if ($timestamp) { // add whatever conditional logic you need here
        $vars['classes_array'][$key] .= ' hello'; // note the space in front of class
      }
    }
  }
}

The following will add the class 'hello' to the li tag. I used a view with machine name 'dates' and a display name of 'page'. The time field is the node created time. You can just install Devel and uncomment the dpm($vars) statement to get what you need. I also left the conditional logic up to you.

Put this in your theme's template.php file:

function MYTHEME_preprocess_views_view_list(&$vars) {
  if ($vars['view']->name == 'dates' && $vars['view']->current_display == "page") {
    // dpm($vars); //uncomment to see variables
    foreach($vars['view']->result as $key => $value){
      $timestamp = $value->node_created;
      if ($timestamp) { // add whatever conditional logic you need here
        $vars['classes_array'][$key] .= ' hello'; // note the space in front of class
      }
    }
  }
}

An alternative method is as follows:

Put this in your theme's template.php file:

function MYTHEME_preprocess_views_view_fields(&$vars) {
  if ($vars['view']->name == 'dates' && $vars['view']->current_display == "page") {
    $timestamp = $vars['row']->node_created;
    if ($timestamp < strtotime('now')) {
      $vars['classes_array'][] = 'bye';
    }
  }
}

and use this views-view-fields--VIEWNAME.tpl.php file:

<div class="<?php print $classes;?>">
<?php foreach ($fields as $id => $field): ?>
  <?php if (!empty($field->separator)): ?>
    <?php print $field->separator; ?>
  <?php endif; ?>

  <?php print $field->wrapper_prefix; ?>
  <?php print $field->label_html; ?>
  <?php print $field->content; ?>
  <?php print $field->wrapper_suffix; ?>
<?php endforeach; ?>
</div>