According to the principle of relativity in physics, the speed of light in a vacuum is constant and independent of the motion of the source or the observer. This principle is one of the fundamental principles of Einstein's theory of special relativity.
In the context of your question, if the source of light moves laterally, the light beam itself does not move laterally with respect to an observer at rest. The speed of light remains constant at "c" (approximately 299,792,458 meters per second) regardless of the motion of its source. This means that if an observer is stationary and a light source moves past them, the light beam emitted from the source will continue to travel in a straight line and not deviate laterally due to the source's motion.
Einstein's light clocks, which are thought experiments used to illustrate concepts in special relativity, involve the measurement of time using light signals bouncing between mirrors. The principles of special relativity apply to these light clocks. The constancy of the speed of light and the independence of its velocity from the motion of the source are fundamental to the workings of light clocks and the relativistic effects associated with them, such as time dilation and length contraction.
In summary, the movement of the source of light does not affect the lateral direction of the light beam itself. The constancy of the speed of light is a fundamental principle in physics, with implications for phenomena like light clocks and the relativistic effects described by special relativity.