In this paper, a new desktop Cartesian-type (orthogonal-type) robot, which has abilities of compliant motion and stick-slip motion, is presented for lapping small metallic molds with curved surface. The size is 850 mm width, 645 mm depth and 700 mm height. The robot consists of three single-axis devices with a high position resolution of 1 μm. A thin wood stick tool is attached to the tip of the z-axis. The tool tip has a small ball-end shape. In order to improve the lapping performance, a small stick-slip motion control is considered in the control system. The small stick-slip motion is orthogonally generated to tool's moving direction. The effectiveness and promise of the stick-slip motion control are examined through an actual lapping test of an LED lens mold with a diameter of 4 mm.