Omega footer navigation
You have to use hook_menu_link_HOOK

For example if your menu is the main menu you could use this example code in your template.php to add class to tag li.

function YOUTHEME_menu_link__main_menu(array $variables) {

  $element = $variables['element'];
  $sub_menu = ''; 
  /* add classes to balise li */
  $element['#attributes']['class'][] = 'grid-3';
  /*$element['#attributes']['class'][] = 'depth-' . $element['#original_link']['depth'];*/
  $element['#attributes']['class'][] = 'menu-' . $element['#original_link']['mlid'];

  if ($element['#below']) {
    $sub_menu = drupal_render($element['#below']);
  }

  $title = $element['#title'];

  $element['#localized_options']['attributes']['id'] = $title ;

  $output = l($lien, $element['#href'], $element['#localized_options']);
  return '&lt;li' . drupal_attributes($element['#attributes']) . '&gt;' . $output . "&lt;/li&gt;\n";

}


To add the class only to the parent menu, you should use a condition to see if the menu item has children. Or make a condition to see if the tag li has the class depth-1 and then add the class grid-3.

The module Menu attributes seems to do the job too.