LiveStreet CMS

var block = $('.js-activity-block-recent');
if (block.length) {
  block.lsBlock('getElement', 'tabs').on('lstabstabactivate', function(event, data) {
    alert(111);
  });
}

А у вас

var block = $('.js-activity-block-recent, .ls-block--activity-recent');
if (block.length) {
  var blockTabs = block.lsBlock('getElement', 'tabs');
  var existsCallback = blockTabs.lsTabs('option', 'tabactivate');
  blockTabs.lsTabs('option', 'tabactivate', function(event, data) {
    if ($.isFunction( existsCallback )) {
      existsCallback.apply(blockTabs, [event].concat(data));
    }
    alert(111);
  });
}

$(function() {
 ...
});