The following HTML allows you to show a video in LightBox2.

<a href="http://www.youtube.com/embed/<VIDEO ID>?autoplay=1" rel="lightframe">Click me</a>

We could control the size of the popup.

<a href="http://www.youtube.com/embed/<VIDEO ID>?autoplay=1" rel="lightframe[|width:320px; height:240px;]">Click me</a>

Done =)

Reference:

• Drupal Module – LightBox2
• Lightbox2 – How to add a lightbox to webpage links