Hi,
The {VAR:LIVE_SITE} tag is replaced automatically when the email is sent by HikaShop to use the URL of your website.
So first please make sure that you have the file
yourwebsite.com/media/com_hikashop/image...ns/icon-48-order.png
If you don't, then it means that the file has been deleted from your website for some reason and you need to add it back or change the path to the image you want to use.
It's also possible that the {VAR:LIVE_SITE} tag isn't replaced with the correct URL if the "live_iste" parameter of the configuration.php of your Joomla doesn't contain the correct URL (for example, if you had put a URL for your dev website and didn't change it when you moved the website to the live URL).
With the Business edition of HikaShop, you can edit the emails via the menu System>Emails. In such case, the changes will be saved as overrides and you won't loose your changes after each update.
With the Starter edition, you would have to copy the files with a .override.php instead of .php in order to not loose the changes.