Double click is a common gesture which is used for various other useful purposes, so that wouldn't be a part of this add-on.

EDIT 2:

In case you are asking about double left clicking on the tab header itself, I believe that is not supported in the new WebExtensions architecture used by Firefox.

EDIT 1:

Double left click (and also triple left click) is very often used for selecting text. Apart from that, various websites use double click for some common UI/UX operations. Hence, in my opinion, such conflicting shortcuts/gesture shouldn't be used.

But, in case you still want such a functionality, you can modify this extension to create a new one by following these steps:
- Go to https://github.com/webextensions/close-tab-by-double-right-click
- Download the code as a zip file by clicking on the "Clone or download" button
- Extract the downloaded zip file
- In the extracted file close-tab-by-double-right-click.js , modify the line which says:
if (e.which !== 3) {
MODIFY THIS LINE TO
if (e.which !== 1) {
- Reference: The above mentioned line can also be currently seen at: https://github.com/webextensions/close-tab-by-double-right-click/blob/master/extension/scripts/close-tab-by-double-right-click.js#L9
- After that, you may zip the files inside the extension folder and use that to create the add-on via https://addons.mozilla.org/ for your use. While publishing, if you wish to use the extension for personal use only, then there should be an option for self-distributed add-ons, you may want to select that.

Hope that helps :-)