By default, Lansweeper doesn't support scanning server core information. However, you can use Lansweeper to retrieve server-core product information through a workaround.
This Microsoft article explains how to check the registry settings to determine if server core is running. As the server core information can be fetched from the registry, you can add this information to the Lansweeper database using custom registry scanning. More information can be found in Scanning registry values with custom registry scanning.
Once the registry information is available in the database, you can visualize it with a custom-built report.