AWS Load Balancer with a static IP address

Question

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

Answer 1

You can attache an additional ENI (Elastic Network Interface) to an instance in your VPC. This way the ELB (Elastic Load Balancer) routes the incoming Internet requests to the web server, and the additional ENI will be used to connect to your 3rd party (or internal) requests (Management network)

You can see more details about it in the VPC documentations