You have:
<link rel="stylesheet" href="https://www.eediete.nl/keuken/wp-content/plugins/lightbox-plugin/lightbox2.css" type="text/css" media="screen" />
This should be:
<link rel="stylesheet" href="https://www.eediete.nl/keuken/wp-content/plugins/lightbox/lightbox.css" type="text/css" media="screen" />
You have:
<script type="text/javascript" src="https://www.eediete.nl/keuken/wp-content/plugins/lightbox-plugin/js/prototype.js"></script>
<script type="text/javascript" src="https://www.eediete.nl/keuken/wp-content/plugins/lightbox-plugin/js/effects.js"></script>
<script type="text/javascript" src="https://www.eediete.nl/keuken/wp-content/plugins/lightbox-plugin/lightboxjs.php?path=https://www.eediete.nl/keuken/wp-content/plugins/lightbox-plugin/"></script>
This should be:
<script type="text/javascript" src="https://www.eediete.nl/keuken/wp-content/plugins/lightbox/js/prototype.js"></script>
<script type="text/javascript" src="https://www.eediete.nl/keuken/wp-content/plugins/lightbox/js/effects.js"></script>
<script type="text/javascript" src="https://www.eediete.nl/keuken/wp-content/plugins/lightbox/js/lightbox.js"></script>
The Lightbox folder inside your plugins folder should be called “lightbox,” not “lightbox-plugin.”
Also, where you have:
<a href="https://www.eediete.nl/keuken/pics/gebakken%20asperges.jpg"title="Caption on image" rel="lightbox[Name]" ><img title="gebakken asperges" alt="gebakken asperges" src="https://www.eediete.nl/keuken/pics/gebakken%20asperges.jpg" /></a>
you don’t need rel=”lightbox [name]” where [name] is only necessary for images in a gallery context. Also, the second part of the image tag above should contain a link to a thumbnail image.