Your state looks to be tough on vehichles without titles. Here is their answer to your question.
If Im not mistaken lost title must be your own, that is to say already in your name.
Now reading off that same site under the general "titles" page I did see where it said they now require atv's and the like to be titled and existing ones would be titled at the owners expense. In theory you could buy it, title it as a dirtbike, and then up it to street legal in later paperwork. I dont know if they would require a mso for that or not.
Either way more trouble than its worth in your case IMO. I just recieved my title in the mail a week or two ago from the exact same situation. Im in Alabama and used the Vermont title service. State of Alabama figured it out and gave me the run around for a while. But got it!