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();