I'm trying to export it and then import it into Google Docs or MS Word

Hi David,

Thanks for reaching out. If your content does not fill the entire page I suggest going to your page setting by selecting the document icon on the right panel. Change the "page size" to a smaller size (you can select custom and make the page as big or small as you would like.) We also have Add-ins that you can use to insert your document into Google Docs and Microsoft Word. Please see this article for information how to insert your doc into Google Docs and this article for information how to insert your doc into Microsoft Word. 

Hi! Lucidchart’s functionality has changed over the years since this post was created, and I wanted to share some updates for anyone else who comes across this post:

First, when exporting, you can choose cropping options to focus on the portion of your diagram that you want to include:

Additionally, you can now also select a portion of your diagram, right-click, and choose Export selection ​​​​​, then a file format of your choice, to more precisely export only certain objects.