He lied to you about clearing things up with the girl.

And he will not clear it in front of you coz he will tell another lie to the other girl.

And he did say its the end of the relationship if you want him to clear things up (in front of you) coz all his lies will be broken then.

When his all his accumulated lies break, there's no point to lie to you anymore. So of course its a bye bye.

Now he is having both girl to pleasure him. And if you wish to continue to do so, by all means continue.
If you dont, stop being so blind