The growth of 3D imaging across a range of sectors has driven a demand for beam steering technology. Fields as diverse as autonomous vehicles and medical imaging can benefit from a high speed, adaptable method of beam steering. We present a monolithic, submicrosecond electro-optic switch as a solution toward the need for reliability, speed, dynamic addressability, and compactness. Here, we demonstrate a laboratory-scale, solid-state light detection and ranging system, using the electro-optic switch to launch modulated coherent light into free space and then to collect the reflected signal. We use coherent detection of the reflected light to simultaneously extract the range and axial velocity of targets at each of the several electronically addressable output ports.