Ally - is it considered a Triggered Modifier?

Next question - If I were going to use Lost City in order for the replacement to occur the power-up has to go on the chain first correct, because the replacement of the Power-up is triggered by the power-up right?

Final question - Would not both Lost City and an Ally power trigger pending on which one is put on the chain first?

Ally powers are triggered powers, yes, and generate triggered effects.

Replacement modifiers, which includes Lost City, don't involve triggers. They also don't use the chain; replacement can occur during a resolving effect. And as the wording of a replacement modifier implies, the replaced event never occurs. "If X would occur, Y instead."

If you have Lost City face-up, Brotherhood characters can't become powered-up, and so they won't be triggering any ally powers.