This depends on exactly what you are asking. Clocks at different heights in an accelerating spaceship run at different rates. This is discussed in the question Which clock is the fastest inside an accelerating body?.
All clocks are affected by the time difference in the same way, so it doesn't matter whether the clock is atomic, a light clock, a mechanical clock or whatever, all clocks at the same height in the accelerating spaceship will run at the same rate. However a light clock is traditionally quite large i.e. the light travels some large distance then reflects back, and we measure the time by the duration of the light beam's round trip. If the light beam travels up the accelerating spaceship then it will pass through regions of measurably different time dilation and the time it measures will differ from the time measured by a more compact clock.
So if the light clock is small, or if it's arranged so the light beams stay at the same height as they travel, then the light clock will measure the same time as all the other clocks. If the light clock is large and the light beams travel vertically then there will be a difference.