This JavaScript can be used to lazy load Youtube videos without WordPress. See instructions: https://wordpress.org/support/topic/plugin-not-activating-how-to-use-plugin-with-youtube-placed-directly-in-theme?replies=4#post-6041175

Lazy Load for Youtube (JS)

/*
 * Lazy Load for Youtube
 * by Kevin Weber
 */

var $lly = jQuery.noConflict();
$lly(document).ready(function() {
  
  function doload_lly() {

    $lly("a.lazy-load-youtube").each(function(index) {
      var embedparms = $lly(this).attr("href").split("/embed/")[1];
      if(!embedparms) {embedparms = $lly(this).attr("href").split("://youtu.be/")[1];}
      if(!embedparms) {embedparms = $lly(this).attr("href").split("v=")[1].replace(/\&/,'?');}
      var youid = embedparms.split("?")[0].split("#")[0];
      var start = embedparms.match(/[#&]t=(\d+)s/);
      if(start) {start = start[1];}
      else {
        start = embedparms.match(/[#&]t=(\d+)m(\d+)s/);
        if(start) {start = parseInt(start[1])*60+parseInt(start[2]);}
        else {
          start = embedparms.match(/[?&]start=(\d+)/);
          if(start) {start = start[1];}
        }
      }
      embedparms = embedparms.split("#")[0];
      if(start && embedparms.indexOf("start=") === -1)
        {embedparms += ((embedparms.indexOf("?")===-1) ? "?" : "&") + "start="+start;}
      if(embedparms.indexOf("showinfo=0") !== -1)
        {$lly(this).html('');}
      else
        {$lly(this).html('<div class="lazy-load-youtube-info"><span class="titletext youtube">' + $lly(this).html() + '</div></div>');}
      $lly(this).prepend('<div style="height:'+(parseInt($lly(this).css("height"))-4)+'px;width:'+(parseInt($lly(this).css("width"))-4)+'px;" class="lazy-load-youtube-div"></div>');
      $lly(this).css("background", "#000 url(http://i2.ytimg.com/vi/"+youid+"/0.jpg) center center no-repeat");
      $lly(this).attr("id", youid+index);
      $lly(this).attr("href", "http://www.youtube.com/watch?v="+youid+(start ? "#t="+start+"s" : ""));
      var emu = 'http://www.youtube.com/embed/'+embedparms;
      emu += ((emu.indexOf("?")===-1) ? "?" : "&") + "autoplay=1";
      var videoFrame = '<iframe width="'+parseInt($lly(this).css("width"))+'" height="'+parseInt($lly(this).css("height"))+'" style="vertical-align:top;" src="'+emu+'" frameborder="0" allowfullscreen></iframe>';
      $lly(this).attr("onclick", "$lly('#"+youid+index+"').replaceWith('"+videoFrame+"');return false;");
    });

  }

  $lly(document).ready(doload_lly()).ajaxStop(function(){
    doload_lly();
  });

});