The present invention relates to a masonry lawn edging block assembly for a multi-grade landscape setting where the ground level of the lawn is lower than the adjacent areas. The assembly includes a plurality of like-shaped straight blocks, outside cornering blocks and like-shaped inside cornering blocks that create a border between the lawn and the adjacent area. The present invention has an L-shaped cross section that includes a vertically extending wall portion and a horizontally extending base portion. Dowels are used to connect adjacent blocks. A series of like-shaped blocks are connected in an end-to-end, end-to-side and end-to-rear arrangements to form the border. The base of each block includes a platform, and these platforms form a continuous deck upon which a conventional lawnmower can travel to cut the grass along the edging block assembly in an even manner and to the same desired height as the rest of the lawn.