Hi Chris! Thanks for reaching out in the community. Lucidchart does support Mind Map imports! For more information on how to do this please take a look at this article. Hope this helps!

The article mentions importing mind maps from MS word or Google Docs  (.txt format only) doesn't say anything about Bubbl.us mind maps which can only be saved as .jpg .png or .html 

I tried importing the .html and only a single rectangle appears from what used to be a massive multi-layered mind map with 50+ rectangles

What am I doing wrong?

Lucidchart only supports the import of Mind Maps from a .txt format. But we're always looking for ways to improve Lucidchart and your feedback is the best way for us to do that. If you would like to be able to import other file types to create Mind Maps in Lucidchart in the future please fill out this feature request form to bring the idea to our product team. In the meantime I would recommend looking into if you can find an online converter that can change your html file to a txt file. Thanks again for your request!