hahahah thank you for sharing your story, i was actually hoping to find an answer here. Coz i have a very good friend who is always late too! But i will share with you 2 stories, that might or might not be helpful. :D
1st one, is from Emily Lam, she's Peter Lam's daughter. Peter Lam is a Hong Kong billionaire, very prominent man in the entertainment industry. Emily once told us that when she was little, she and her siblings couldn't get up in time on Sunday mornings to go to the church. To teach them a lesson, their mom would leave the house without them and not allow them to eat for the whole day. But most importantly, her mom would patiently explained to them why she did so, "Time is most precious in life, and everyone's time is equally precious. Respect the other's time as well as yours." She has been a punctual person since then.
2nd story, is from another friend, who happens to be from a very wealthy family too, in Singapore. His method is unconventional but certainly works for some! When we go out for dinner with him, whoever is late, must drink 5 seconds of whisky/brandy from the bottle.. it's pretty lethal, so many friends have learned to be punctual when hanging out with him, at least.
My conclusion is, always be punctual no matter what. Bring a book, or read something on your phone/tablet if the person you're meeting is late. Because you can just relax and learn something new, consider it as spending some quality time on your own. It's easier to change ourselves than trying to change the others. But if you have kids, it's important to help them build good habits from young! :D