Use left and right arrow to rotate the grid. Press space to reset the rotation. Draw lines with the mouse between grid points. Press Z to undo the last line (you can delete several by pressing Z again). You can rotate the grid after drawing and the lines rotate with the grid.
Credit to Jacob for the idea. Note you can draw lines that are off the side of the grid, but they might not rotate properly. To rotate the grid, I used a standard matrix transformation for rotation about an angle. This transforms the standard grid to a rotated grid. To snap the mouse to the grid, I rotated the raw mouse coordinates in the opposite direction, rounded them to the nearest standard grid point, then rotated them back.