Hi ​@jbass 

While individual documents can be moved from My Documents to Team Folders by dragging them, entire folders cannot be moved directly.

Please refer to the similar topic for your reference - Move a Lucidchart document to a shared folder in Lucid | Community

A document admin or account owner can navigate to the Compliance page of the admin panel to use Discovery to transfer your documents to a Team folder in bulk. 

Hope this helps - Happy to help further!!
Thank you very much and have a great one!
Warm regards

Hi ​@jbass, thank you for your post and ​@Humas1985 for sharing resources. I’m happy to share more information about the issue you’re experiencing:

As outlined here in the Team Folders article, regular users cannot Can move folders in and out of a team folder with Edit & Share permissions - only Account Admins and the Account Owner can do this. 

However, if you have Edit access to the Team Folder, you can still move documents in and out of the team folder. 

I hope this helps. Please feel free to let us know if you have any further questions!