Use Tumblr's built-in lightbox for displaying high-resolution images in a lightbox, basically "free" by leveraging code already in Tumblr. Updated for 2018: no longer requires jQuery, gets `low_res` attribute from image `src`, use more modern JS standards than when this was originally written in 2014!

tumblr-lightbox-for-photos-2018.html

<script>
  let clbPhotos = document.querySelectorAll('.page-index .photo-image[data-highres]'); // Replace this with the selector for whatever you want to be the trigger.
  Array.prototype.forEach.call(clbPhotos, function(clbElement, i){
    clbElement.addEventListener('click', function(){
      let clbAttrs = clbElement.dataset;
      let clbData = [{ 
        "width": clbAttrs.highresWidth,
        "height": clbAttrs.highresHeight,
        "low_res": clbElement.src, // My trigger is the image element so I can take the existing src that is currently being displayed. This is quite good for performance because I know that version is already loaded in. If you make the trigger anything else, you'll need to find another way to provide the low resolution version, it's not optional.
        "high_res": clbAttrs.highres
      }];
      Tumblr.Lightbox.init(clbData, 1);
    });
  });
</script>

Example usage: 

<img src="{PhotoURL-500}" class="photo-image" {block:HighRes}data-highres="{PhotoURL-HighRes}" data-highres-width="{PhotoWidth-HighRes}" data-highres-height="{PhotoHeight-HighRes}"{/block:HighRes}>

Working demo: https://codepen.io/edadams/pen/gQQVOj?editors=1111

About:

Tumblr exposes a function called Lightbox.init that lets you trigger a custom lightbox with whatever you want in it. On the Tumblr Dashboard, apps, and default theme, clicking on an image will show the full-size in a nice lightbox. That function can be used custom as seen above. 

The magic lies in the data-highres-* attributes that I have added to the image. I'm looking for any images with a data-highres attribute, as well as several others that are necessary for the lightbox function to work. Mercifully Tumblr exposes all the data you need for you.