Lounge Access? YUL-LGA-ORD-LAX

Hi all,

Apparently I'm a sucker for layovers. YUL-LGA-ORD-LAX all within the same day. It's booked with all legs as First (and "Business" for the short YUL-LGA leg.

Do I have lounge access at ORD? Even if the international portion of my itinerary was two segments prior? And for those who have been to ORD, which lounge is the best one in your opinion?

For LGA I'm thinking of spending most of my time at the Chase lounge during a my 4-hour layover. Is the AC worth stopping by?

Finally, I arrive at LAX at 10:37pm. Would I get AC lounge access upon arrival? Would that include the Qantas F lounge if I walk over to TB? I'm OW Emerald through Alaska and I've never had the opportunity to use this lounge because I'm usually just flying domestic, but it's my first time on a cross-border flight on AA metal ticketed as business so maybe that works?

I'm also a fake AA Platinum through non-flying means, which is new for me (thanks surveys!). I don't know if that helps with access. All these rules really muddle me up...

Thanks for all your input!