The light month is the distance that the light travels in vacuum in one month and so is a unit of distance. According to the IAU one month is defined as 30 days with 86400 seconds each day.
Similar units are the light second, light minute, light hour, light day, light week, light year.
Unfortunately there are no distances in nature where it make sense to express them in light months. Distances in our solar system are normally expressed in light seconds up to light days. Distances in our galaxy are normally expressed in light years.