Look, it's going to happen. You will be late at some point. Here's what to do when that happens.

Sincerely apologize. Express human remorse for wasting someone else's time.
If you decide that you want to give an excuse for your lateness, explain it briefly and move on. Excuses are fine, but long excuses? They're typically boring and no one cares. Just own up and repeat #1.
If you're more than twenty minutes late, buy that person something. A drink. A chocolate. Something. It's kind and really lets the person know that you're sorry and that you don't take them for granted. No one wants to feel like that loser who's waiting for some rube to show up. It's a shitty feeling.
Believe that you can do better next time. Make an effort to specifically not be late the next time you see that person.
Never believe or say the phrase, "I'm always late." Why? If you say this to another human being, and expect to have any ounce of respect thrown your way, you're a maniac. You have control over being on time or late. You do. We all do. We also set expectations for ourselves, and if this is what you're declaring about your own character? Wow. You deserve unhappiness. You really do. It's also abnormal to blindly just accept this trait. Not only do you have low expectations of yourself, but you're also telling others that their time isn't as important as yours - which is wildly obnoxious. If you've said this statement to people, you should consider yourself lucky that you have any friends at all.

Can people change? Can the consistently-late people of this world change? I have to believe they can. I've been late before and I'll be late again. But if I'm ever KNOWN for that behaviour? Someone lock me up. It's so arrogant to be confident in one's lateness and to just assume others will adjust to it. That kind of selfishness is what turns people into serial killers. Right? Too much? No, I'm right.

Also? If you think I'm talking about you specifically, that's hilarious. I can picture a few certain people I know reading this and thinking, "Yikes, she wrote this based on me" - maybe you're right, maybe you're wrong. I guess we'll never know.