There is not a way to auto layout an org chart as shown in your example. There are only three layouts available in our org chart feature. 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.
Note: apologies for the delayed response here. Our forum host experienced a bug that impeded our ability to respond publicly. However, we wanted to ensure the resolution provided in our 1:1 email support with you was provided here in order to assist other Community members who have similar questions.