Not irrelevant at all, Laurie. Using a lid is a good idea - I’d always use one when raising the temperature of the top of the food is a concern; it’s going to block the temp sensor though, so I didn’t do it this time around.
Even at fairly low heat, the pan and the air inside - when the pan is covered - will be plenty hot to cook eggs. I think a lot of “the secret” is really getting to know the stove, even the individual burner. The thermometer can help there, i.e. as with a gas burner there will usually be some guesswork as to how hot the pan is really getting.