DWG ("drawing") is a binary file format used for storing design data and metadata. It is the native format for several CAD packages including AutoCAD. The file format specification is not publically available and it is not natively supported by the LayoutEditor. However, it can be used through a converter.
With version 20150718, the LayoutEditor automatically triggers the ODA file converter (former TeighaFileConverter) if it is installed on your system. DWG files can be loaded and stored as any other file format. To use DWG, please install the converter on your system. It can freely be downloaded from this link.
Other converters can be used, for example this online converter from Autodesk https://www.autocadws.com/. Other converters can be integrated into the LayoutEditor by using macros.