I don't need to dream of being late. I usually am in real life anyway.
I have weird dreams of being early. Of arriving at work at first light, something like 6 am, and the place being shuttered up. Of getting in and there being nobody around for hours.
Another one is being back at school, like I've gone back to repeat the last two years of high school so that I can get better marks for some reason. And realizing that I have somehow not attended any classes for key subjects and I am hopelessly lost.
Another one is being back at the house I lived in from the ages of about 10 thru 22. And finding out that one of the first cars I owned is still there (behind the garage) and still driveable, and I start driving that around. And it's weird because the car is so old and dusty and has an engine literally 5 times as big as the car I have now (5.8 litres, or 351 cubic inches, compared to 1.2 litres now).
Another one is going back and buying one of the 2 houses I grew up in, and the house being exactly the same as before, just a bit more wear and tear.
I also have "hybrid people" in my dreams. Like someone who is a mixture of 2 or 3 people who have been a key part of my life. Usually female.