My experience is that the lid starts out colder when the meat is cold and approaches the grate temp as the smoke proceeds.
This is not a matter of opinion. It is what I see. It must be something that depends on subtle differences in technique or perhaps how the probe is located or meat arranged. Others who experience higher lid temps cannot be wrong either.
As others have said, it doesn't really matter. What does matter is that you become accustomed to how your readings go and don't obsess about them but rather learn how they affect your results. To that end, I highly recommend keeping a log of every smoke with notes on time vs. temperature and anything else you might want to reflect on when you plan your next smoke. I tend to rely on the grate temperature and use the dome temperature as a cross check.