Hi there Jason thanks for reaching out! Unfortunately what you are trying to do is not currently supported in Lucidchart. However we're always looking for ways to improve Lucidchart and your feedback is the best way for us to do that. Would you and anyone else interested in this idea mind adding it to our feature request form? Ideas submitted to this form are passed on to the product development team for their consideration.

As a workaround I would recommend you to download what you want to display as images and insert them into the Doc. To do this set the layer visibility for the first image then click sync visibility in the layers panel. This will allow you to download a PNG or JPEG with the current visibility settings. Repeat this process to download images of all the states you want to display and then insert these into your Google Doc.

Thanks for your response Eric. I filed the feature request. It's helpful to know the feature doesn't already exist (i.e. I just can't figure it out). I had originally thought to make copies of the Lucidchart diagram itself and inserting the copies into the Google Doc. But I'll try exporting PNG files instead and doing it that way.

Unfortunately this isn't working well. When I try to download a PNG all layers of the doc are included. I can't find a way to only export selected layers.

+1 to this feature request