Yes! The map data in LANDSCAPE can be exported to ESRI Shapefiles (.shp).
Click the Export data button on any map in LANDSCAPE:
You will be presented with choices of which layer to export. Each type of geometry (polygon, line, point) has to be exported as a separate shapefile.
Choose a layer, then click Export. Your data will be converted and a link will be generated to download a .zip file that contains all the files that make up the Shapefile.