WPE Produces many molded shapes of cast basalt on Earth. They use a special grade of natural basalt that melts near 2372 degrees F (1300 degrees C). This product is advertised to have a density of from 2.8 to 2.9 g/cm3 a hardness of 8 Mohs a compressive strength of 400 to 450 MPa and temperature resistance up to 662 degrees F (350 degrees C).
David Dietzler has an article at moonminer.com that refers to casting basalt bricks on the moon. Corundum made on Luna could be used for abrasive machining of bricks. They can be ground flat and square simply by rubbing the bricks together in pairs with local grit between them. More complex shapes than rectangular solids will require grinding wheels that should be produced from local materials. They need to contain a considerable proportion of grit harder than basalt.
It may be possible to join cast basalt bricks with lunar cement if the structure being made is not for the purpose of containing oxygen, water, or water vapor.