If a message is deleted, not archived, it is deleted for good. There are some things you can try!
1. Check your GMail chats folder to see if you maybe have a backup of the conversation. https://mail.google.com/mail/u/0/#chats
2. You can ask the other party to check the same if they dont still have the conversation history. If they do, they can copy/paste/email it to you.
3. Double check to make sure you didnt Archive the conversation as well!