Currently, you cannot remove your own posts or threads from LiveWire. However, you do have a few options available if you have an abundant need to have your topic or reply removed:
Message A Moderator - Moderators will remove/mark anonymous a select few topics or replies if a valid reason is given.
Mark Anonymous - The anonymous feature can be used as an alternative to having your replies/topics removed but only when the topic itself is archived, which is relative to every forum. To check if your topic is archived, scroll to the bottom of the page on any opened topic and click "Go Advanced," then look at the top for a highlighted banner that says your topic has been archived.
Edit Content - Feel free to edit your topics/replies completely if there is a need.
Between these three options, you should reasonably be able to hide particularly sensitive information.