Christina,
Option 1, Sending the Responses in an Email
I went ahead and created a version that adds an "Email My Journal" button to the Learning Journal. It opens up a pre-filled email and the user only needs to click send. (Rt-click and save the file)
Learning Journal with Email Button
Option 2. Sending the responses to the LMS
This would be great functionality. I personally don't know how to make that work. Here's some links, though, that will give you a start.
Javascript error and LMS
lmsAPI Functionality in HTML5 Output
Rise: How to Report Completion and Success Statuses to an LMS
Have fun journaling!
Mike