Hi Dan thanks for posting in the Lucidchart Community! Unfortunately default styles are currently not applied to lines in mind map. However we're always looking for ways to improve Lucidchart and your feedback is the best way for us to do that. 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.

As a workaround you will need to select all of the lines in your mind map to apply the styling you are looking for. The best way to do this would be clicking and dragging or using Ctrl+A / CMD+A to select all of the shapes in your mind map and then applying the line styling. 

Thanks for your request and I apologize for any inconvenience this causes you.