Me and my lady friend had sex early this morning (Wednesday, 22 Aug)... and we need to urgently decide whether she needs to use the morning after pill or not, since we do not desire a pregnancy, but also feel uneasy with the concept of ending the pregnancy (with the morning after pill).

Here are the facts:
-No condom was used.. but she is on the pill.
-Her last period was between last week Tuesday and Saturday.
-She takes the pill usually between 22:00 and 23:00.

-Now the problem is, she took the pill late on Sunday... about 3:00 Monday morning.
-The pill she was suppose to take Monday between 22:00 and 23:00, she also took late, some time in the early morning hours of Tuesday.
-Tuesday she took the pill a little early... about within an hour before 22:00.

As I said, we had sex in the early morning hours of Wednesday. Now the bottomline question is: what are the chances that she will become pregnant?

The morning after pills only prevent pregnancy. If a woman is already pregnant, they do nothing. Note that they are also called Emergency Contraceptive Pills (ECP).

As for is she even needs to take them, it's hard to say. She wasn't even a full day late either time. If she reads the insert that's supposed to come with her pills they would tell her what to do depending on how late she is. Usually they don't advise any extra precautions if you're less than a day late.

[deleted] but going to the original question:
It depends a lot too on which part of the cycle she is. During the first week the chances af pregnancy are much lower than the other two weeks, so you should be rather safe if she is in the first weeks.
I am rather good about the time in which I take the pill, but it has happened to me that I've taken it 3 hours late in one occasion and nothing happened.