One of our guys figured it out:
Download and unzip the Visio file from https://wiki.splunk.com/Community:Splunk_Visio_Stencil
Open your LucidChart diagram
Click the "Shapes" gear on the left side of the ribbon (just under the File menu)
In the lower left, click "Import Shapes"
Click "Add to New Library"
Select the unzipped .vssx file from the first step
Then click "Use Selected Shapes" and they should show up in your file
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