Welcome to FT rdu9!

Now you have unfortunately learned about one of the pitfalls of booking through a third party site.

So, your main problem is you now arrive at MIA at 7:30 p.m., and your MIA-RDU flight leaves at 4:30 p.m. It's not clear from your post if you were just placed on another LAN flight, or if your original flight was cancelled. I don't know your exact travel dates, so I couldn't look at LAN's webpage to see if an earlier flight was available.

There is a nonstop AA flight MIA-RDU at 8:55 p.m. It would be tight, as you'd have to clear immigration, customs, recheck your bag and get to your next flight, and MIA can be a zoo.

Is this booked on one ticket? Is it an AA ticket? If so, why is anyone talking to LAN? Have you asked Orbitz to rebook you on this AA flight, or even the first AA flight the next morning?