It will play if you set it to autoplay in a muted state.
 For autoplaying would be to instantiate the player with an empty video on page load:
var player = new YT.Player('yt-media-player', {
  height: height,
  width: width,
  videoId: ''
});
Then on the click event of opening the lightbox you can load the particular video and call it to play:
player.loadVideoById(youtubeId);
player.playVideo();