I'm chronically late, but usually no more than 30 minutes and generally less than 15 minutes. I have no sense of time, or rather, my sense of time isn't in sync with actual time. Thirty minutes can take two hours to pass if I'm bored or five minutes if I'm absorbed in something. I set all kinds of alarms on my cell phone for kid-related stuff because I'm paranoid about missing an important pick up/drop off time.
My husband and my three older kids (INTP, INTJ, INFP, E?T?) all hate being late and are conscientiously punctual. The youngest one I'm not sure about how he feels about punctuality yet.
“There are two novels that can change a bookish fourteen-year old’s life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs.” ~ John Rogers
I am like an ENFJ/INFJ hybrid but closer to ENFJ. I am always almost late to everything. Strong Ni can be a curse. If I am engrossed in something, I want to continue doing it rather than doing what I am supposed to be doing next. Typically, it's like this. 5 more minutes is going to be ok. 5 minutes is up. It will be all right if I do it for 10 more minutes. 10 minutes is up. Well, 15 more minutes won't make a difference. It continues and continues until in the end, it becomes "Oh shit, I should have gotten ready 30 minutes ago".
The INTJs I know tend to be on time only if they consider it important. This behaviour in particular (ditching you to go to a restaurant, without telling you let alone asking if you wanted to come?) is pretty ridiculously rude, except perhaps if your meeting was extremely casual.
Have you considered that she could be istp, which can resemble intj in thoughts and behaviour? It's funny but istp is often more like intj than either is like intp (in my experience) - perhaps the shared Ni/Se. Your description didn't include much about being abstract which is why I'm mentioning this. ST is as "cool, rational and understanding" as NT.
Agreed. I'm almost always late (by a maximum of half an hour), but if I honestly want to be somewhere I'm there ten minutes early, guaranteed.
Gandalf was an INTJ. He says, "A wizard is never late, he arrives exactly when he intends to." Unfortunately for the rest of us (the ones who realize that we aren't the center of the world) it's important to be on time for a variety of reasons.
Kidding, I love INTJs. I'm late sometimes, but not out of entitlement or arrogance. It's just my P preference coming out. I just don't care that much.
And come on . . . she's late because she's a girl, not because she's an INTJ.
I don't know about others but I know I'm never late for something that I think it's important to be there on time. In that case everything is well planned in advance so that I can get there on time. But I can be really late for something that I secretly want to avoid.
I don't mean to imply that she secretly wants to avoid you but if she really is an INTJ who trusts you and you confront her about this, I believe she should already have a well-thought explanation for you.