LiveAgent checks if the received email was sent as plain text or as an HTML email.
If the email was sent as plain text, LiveAgent automatically converts all URLs in the email's body into clickable links.
However, in the case of HTML emails, LiveAgent doesn't search for URLs in the email's body to automatically convert them into clickable links.
The reason is that if someone is sending an HTML email, they should format it to the desired form, so it would be displayed on the recipient (LiveAgent) side exactly as it was formatted and defined in the HTML code (or via WYSIWYG editor).