I have a set-up running on Amazon cloud with a couple of EC2 Instances running through a load balancer.
It is important that the site has a unique(static) IP or set
Your outbound requests to your 3rd party APIs will NOT go out via the ELB/ALB. That's for incoming connections. If you need an inbound static IP you'll probably need to forego the loadbalancer (or figure out how to implement Anshu's suggestion to attach an elastic IP to the loadbalancers, the doc is light on details). Update: I found some documentation that ALB use static addresses (and I just tried binding an elastic IP to one to be sure and that failed). If you're talking about outbound connections see below: