Unless the lid thermometer has a probe which extends down to near grate level I don't think they will be "accurate", depending on where in the dome you're measuring. But of course, it's not practical to install a built-in lid thermometer with a 6" stem.
I like to use a long stemmed thermo with a clip through the vent hole.
To get down to grate level, I have used a long turkey fryer thermometer. But the lid thermometer from Weber works pretty well too, I add ~50°F to what the therm says to estimate what the grate level temp is.