Is corret this dialogue
A: I have to go because I am meeting with a friend.
B : What time are you meeting?
A: in five minutes, so I must hurry because I am late
B: Do you want a lift?
A :Please, do! I owe you one

Question

Is corret this dialogue
A: I have to go because I am meeting with a friend.
B : What time are you meeting?
A: in five minutes, so I must hurry because I am late
B: Do you want a lift? 
A :Please, do! I owe you one

Answer

A: I have to go because I'm meeting a friend. (no 'with')
B: What time are you meeting?
A: In 5 minutes, so I must hurry because I'm late.
B: Do you want a lift?
A: Please... yes. I owe you one.

Overall, your version is excellent.

Answer

Minor correction - Is this dialogue correct ?

Yes on the whole, it is correct. The very last sentence "Please, do! I owe you one", I suggest that "Yes, please ! I owe you one" or "Please ! I owe you one" would be more often encountered.