A conventional spherical acoustic lens is modified by restricting its aperture in the form of a slit to provide directional sensitivity. The spacing between the two parallel absorbing sheets forming the slit is adjustable to obtain varying slit widths. The resulting lens can be used in conjunction with V(Z) method to obtain leaky wave velocities of the sample under investigation as a function of direction. The theoretical V(Z) analysis of the lens involves a two-dimensional integral rather than one-dimensional integral of the conventional lens. Single crystal anisotropic materials are chosen as test samples. Reflection coefficients for anisotropic single crystals of given surface cut and orientation are calculated. Numerically evaluated V(Z) curves are used to deduce the surface wave velocity of the object for the given orientation. This is compared with the surface wave velocity directly calculated from the elastic parameters of the object. Results show the compromise between signal-to-noise ratio and angular resolution as the slit width is varied. V(Z) measurement results of a slitted lens are presented to be compared with calculated curves. The new lens is used to measure the acoustic velocity on the (001) surface of GaAs along varying directions with differing slit widths.