What time is it when a celestial object crosses the meridian (or is there enough information to answer this question)?
A meridian would reference a center line or middle of a certain spectrum. Our Prime Meridian, for example, is the center of the globe by which all distances either East or West are based off. The meridian we could use to tell time would be the center of the sky.
A celestial object would include objects such as the Sun and the Moon. Each can be used to keep track of time, each with their own schedule. When the Sun is at the meridian, its highest peak, it is noon or 12 o'clock PM. When the moon reaches the meridian it does not count our time on our clock, but instead references middle/end of a day on a 28 month calendar, or a calendar based solely off the progression and movement of the Moon.
If we are not being told which celestial object we are following then there is no way that we could tell which time they are referring to in the question. These two examples alone are conflicting units of measurement and cannot be compared easily as 1 Lunar day is of a different length than 1 Solar day.