@scoobycute Thanks for asking and in a nice way. I love things like this. I'll drone on about my habits but I promise I'll try to help you deal with your late friend 
I can be on time when I need to be -films, trains, planes etc but generally arrive up to 15 minutes after we have arranged to meet. I do not consider this to be late. I sometimes arrive up to 10 minutes before but in general I don't.
I'm good at planning journey times by counting backwards, factoring in door-to-door times and making a reasonable but not excessive allowance for delays like expecting the streets to be more crowded at 9am and 6pm than 11am or 9pm. Public transport is frequent and reliable where I live. I prefer to take buses than tubes because the view is nice but tubes are better in times of heavy traffic. I also walk quite a lot and know exactly how long that is going to take. I once had a job where I was 30 minutes' late on the first day which I was embarrassed about for a short while but once I had apologised I considered the matter closed. It was because I didn't realise how heavy the traffic was - roadworks. The next day and days thereafter I walked even in the rain. It was a nice walk and much better for me. It was about 40 minutes - 10 minutes' more than the advertised journey time but far less stressful than being stuck on the bus. I was still up to 15 minutes' late though.
Other latecomers give other reasons but I am late because I waste time. I do things - reading just one more article, water my plants, put the washing away - rather than getting ready. I can't speak for others but that is my honest answer and I think people who say it's not are possibly not telling the truth.
I could stop doing it but unless I am going to miss a plane I don't. I am always late for work by about 15 minutes. I've always done it and don't feel guilty about this. I don't drive a train or work in a shop or any of the many other places where you have to be on time. I am a good worker in other respects. Not as good as some but better than others.
Here are my tips for late management:
Always meet somewhere you can do something else in the meantime.
I have a very good friend who is generally about 20-30 minutes' late so later than me. We arrange to meet places where there is something for me to do. Films and dinner afterwards work for us. If the film is starting I'll go in and we'll meet at the end and go to the restaurant. It's not as if we were going to chat during the film so we don't need to be together. I have another friend, also a film fan, who turns up 30 minutes before the doors open even though it's always the same place so she knows how long it will take to get there. But she doesn't like to be late and if she's waiting around that's up to her.
My late friend has been later so has missed planes either because she has got to the airport too late or been faffing in duty free. She once turned up at the correct time but 24 hours late. This wouldn''t happen with me because I would know when we had to be there and would just leave if she wasn't ready. She knows this.
My husband, MIL and BIL are habitually over early which is very annoying. They will arrive places with at least an hour or more to spare. Not built-in emergency time for unforeseen circumstances but actually two hours waiting outside somewhere and rattling on the locked doors. They regard anyone who doesn't do this as late and get passive aggressive about it.
This is not prompt timekeeping and wastes people's precious time just as much as being late does. Luckily he doesn't do it as much as his family does because I will not do that.
I have been offended when I arrived at a restaurant 15 minutes after my booking to be scolded. I asked the waiter if he wanted me to leave and he said no and I said "okay I'll sit down". If they don't want me to come back them I won't and will spend my money elsewhere - no hard feelings just don't sulk and don't tell me off especially not in front of people. It's a regular place and the person had taken it upon himself to boss the customers into line said his partner.
Back to your friend. If you want to remain friends work out some of the things we do so you're not hanging around like a lemon. Or lie about times - it irritates me for a moment until I realise I have no right. If you don't want to be friends any more drop her with no guilt. Don't waste a lot of time trying to work out why she is like she is and definitely don't listen to those people who say that being late is because she thinks her time is more important and really because she thinks you're worthless. It's not.
Just decide whether it's worth seeing her any more.
PS the reason I could spend time on this long post is because I cooked the dinner hours ago and did all my housework and weeding. It's a chilli that I just have to warm up and cook the rice. I am very organised when I want to be.