Hi April

Thanks for reaching out. Unfortunately putting the swimlane headings on the right side is not currently supported in Lucidchart. However this is an excellent idea and may be helpful to many users. Would you mind adding your idea to our feature request form? Ideas submitted to this form are passed on to the product development team for their consideration. Thanks for your request and I apologize for any inconvenience this causes you.

To learn more about how to use swimlanes take a look at the Diagram with Swimlanes article in our Help Center.

Would also very much like this feature. 

Thank you Ben! We've logged your feedback and would love to see any additional details about your use case or what you'd like to see out of this experience in this thread.