[Idiom] it's on me

[birdeen's call]

Hello.
Here's an excerpt from one book:

"I'll wait outside for you, Tizzoni," Cappelli said to Renato. "And it's your turn to pay."
"I thought it was your turn," said Renato.
"Next time is my turn," Cappelli said. "Next time, if it happens, it's on me."

The context didn't make me certain of the meaning of the phrase "it's on me".
My first guesses were two:
1. it's my turn
2. i'm obliged to do it, it's my duty.

On the web, I found only an entry in "Urban Dictionary". I can't post a link because of my post count.
It fits the context perfectly. But first of all, I can never be sure about the value of this particular dictionary's entries; and second, I'm wondering if there are any other or broader meanings of the phrase.

 

[Raymott]

Hello.
Here's an excerpt from one book:
The context didn't make me certain of the meaning of the phrase "it's on me".
My first guesses were two:
1. it's my turn Yes
2. i'm obliged to do it, it's my duty. "It's up to me" is the idiom for this.
On the web, I found only an entry in "Urban Dictionary". I can't post a link because of my post count.
It fits the context perfectly. But first of all, I can never be sure about the value of this particular dictionary's entries; and second, I'm wondering if there are any other or broader meanings of the phrase.

"It's on me" simply means "I will pay". It doesn't necessarily have the connotation of being anyone's turn. For example:

A: "Let's have dinner at the Ritz"
B: "Sorry, I can't afford that."
A: "Oh, it's on me."
B: "OK, sounds great. Thank you"