On the Firebug Lite website there is information on how to write an extension for Firebug Lite, but it doesn't say how to deploy that extension.
I read that deploying an extension for Firebug is like installing a plugin in Firefox. Is it gonna be the same for an extension of Firebug Lite?
You should be able to extend Firebug Lite by simply including your script on the page as shown on the Firebug Lite website:
To include your extension the code needs to be executed after Firebug Lite is loaded. E.g. this can be done by saving the code above into a file and include it via a
<script>tag after including Firebug Lite: