In order to enlarge the capability for in-plane manipulation of the Bloch surface wave (BSW), we investigate 2D gradient index (GRIN) optical components using a finite-difference time-domain (FDTD) numerical method. To ease difficulties in fabrication to acquire a continuous index profile of GRIN optical components, we propose a stepwise index profile. For 2D surface wave devices, such discrete index steps can be achieved by stepwise structuring of the top layer, also called the device layer. For the demonstration of the stepwise GRIN optics concept, we consider a Luneburg lens, which is a good example of the GRIN optical component that produces a strong focal spot on the shadow-side curvature of the lens. The limited index contrast of the BSW systems loosens the confinement of the focal spot. A mitigation plan is to elongate the circular geometry to the prolate ellipse. BSW-based Luneburg lenses with a relatively small number of steps and an elliptical geometry are demonstrated with comparable performances to a standard Luneburg lens.