UPDATE:

I was wrong the direct upload does not work either. It just seems to because the image appears and I can manipulate it and then it just disappears.

Doing some spelunking in the docs suggests that LC has a 5MB upload limit. Given that my image is 5.9MB I see why it would be disallowed. There is still a bug worth fixing here IMO because it would be easy to just produce an error message that explains that rather than just fail unhelpfully.

I still have a problem. Even though I convert the image to a <5MB JPEG which loads up fine LucidChart randomly degrades the quality so that it is entirely pixellated. The end result is horrible. I am trying to import a high-fidelity image so that I can build a diagram where I point things out with callouts but if the viewer cannot see the detail in the image the callout is useless. Is there any way to tell LucidChart I need the full resolution image?

I can't understand this design decision.

ORIGINAL JPEG

AS DISPLAYED IN LUCIDCHART

Hi @matt t101 thank you for posting in the community! Just to make sure that we are on the same page please review our Work with shapes in Lucidchart and our Shape Libraries article from the Lucidchart Help Center and let me know if you have any questions about the set up or intended functionality.
 
Problems with uploading could be related to the size of your image. Would you mind resizing your image and trying again? -- we have a size limit of 4000 pixels.

I recommend resizing or compressing the image in order for it to upload.  A quick workaround is taking a screenshot of the image and uploading the screenshot. 
 
Please let me know if this is not the issue or if you continue to run into trouble uploading images.