Если все так, как написали, должно работать
<div class="lives"></div>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.4/jquery.min.js"></script>
<script>
var data={"LI_site":"devaka.ru","LI_month_hit":"109891","LI_month_vis":"49790","LI_week_hit":"26620","LI_week_vis":"14228","LI_day_hit":"5207","LI_day_vis":"3393","LI_today_hit":"335","LI_today_vis":"232","LI_online_hit":"11","LI_online_vis":"6"};
$('.lives').html(data.LI_site);
</script>
Может, jQuery не подгружена?