Snakes and their bio-inspired robot counterparts have demonstrated locomotion on a wide range of terrains. However, dynamic vertical climbing is one locomotion strategy that has received little attention in the existing snake robotics literature. We demonstrate a new scansorial gait and robot inspired by the locomotion of the Pacific Lamprey. This new gait allows a robot to steer while climbing on flat, near-vertical surfaces. A reduced-order model is developed and used to explore the relationship between body actuation and vertical and lateral motions of the robot. Trident, the new wall climbing lamprey-inspired robot, demonstrates dynamic climbing on flat vertical surfaces with a peak net vertical stride displacement of 4.1 cm per step. Actuating at 1.3 Hz, Trident attains a vertical climbing speed of 4.8 cm/s (0.09 Bl/s) at specific resistance of 8.3. Trident can also traverse laterally at 9 cm/s (0.17 Bl/s). Moreover, Trident is able to make 14\% longer strides than the Pacific Lamprey when climbing vertically. The computational and experimental results demonstrate that a lamprey-inspired climbing gait coupled with appropriate attachment is a useful climbing strategy for snake robots climbing near vertical surfaces with limited push points.