IIRC, all we support are GET and POST. None of the WebDAV verbs are supported.
Thanks Eric, thought that might be the case. I guess the easiest solution would be to do a post to one of my own sites and then do the delete to the 3rd party from there, passing back the response to my plug-in.
Look at the 4th parameter to LrHttp.post. It allows you to specify as a String what method to use. If omitted it uses "POST" but you can provide your own value there, e.g. "DELETE"