what is the nature of your "land grid"?
Is it a fishnet of intersecting lines?
Is it a polygon FC with tiled rectangles?
If they are polygons, the polygon's extent object will tell you the lower left corner coordinates of the square you have selected,
and will even return a point object for the lowerLeft (or whichever corner you fancy as 'origin')
If the grid a fishnet of lines, you can create intersection points by using Planarize Lines,
then collecting the four closest points to your cursor click.
These four will be the corners of the grid sqaure.
Some math comparing the point coordinate values will give to the corner you want.