Hi Ed thanks for posting in the Lucidchart community - we're glad you're here! By default adding text to a basic shape like a box will center the text in the shape. Currently this can only be adjusted within the space that the shape encompasses using the text alignment tools.

Unfortunately repositioning the text outside of these nine options within or near a shape isn't currently possible by dragging and dropping. Instead to achieve the final result you're looking for I would recommend deleting the default text within the shape then adding a new separate text box. This can be positioned exactly where you'd like in relation to your shape. Then you can group the shape and the text box together so that they still behave and move as a single unit. I've demonstrated this in the GIF below. 

Finally if that sort of text + shape combination is one you'll utilize frequently I'd recommend saving it as a custom shape. This way you can easily drag and drop the text + shape combo onto your canvas anytime you need it. For more information on how to do this please refer to our Shape Libraries article from the Lucidchart Help Center and post any additional questions below!

Thanks for the quick response.