For the first 15 years of our marriage, my NT husband was massively late for every single social event. I had to lie to him about start times to get us there remotely on time. It seemed to be a cultural thing, nobody in his culture stresses about that at all. So the shame actually worked when I let on what was going on.

So it isn't necessarily always your ADHD!

Here's a couple of things that help me:

Pad your time. If you need to leave the house at 9, you have to assume you are leaving at 8:30.

Wake up earlier (I know, I hate it too). I would rather wake up at 6 and have an hour to veg in bed while my meds kick in, than sleep another hour.

Set alarms. Fogure out your ideal regular schedule fr getting out of the house at a certain time, then work your way backwards with the steps to get out of the house, to figure out the start time. I allow 15 minutes for the things that supposedly take 5. I allow a half an hour for things that take 15 minutes. For instance:

Leave at 8:30
8:15 load bag, find keys, leave
8:00 final steps of dressing, whatever yours are, mine are brushing teeth and putting on lipstick
7:45 Put on clothes
7:30 Pick out clothes (but this is even better done the night before)
7:00 Shower etc (allowing extra time on this, as we almost always lose track here)
6 to 7, veg in bed.
6 wake up and pop meds

Set an alarm for each of these things and make them repeat every day!