The ip addresses of your load balancer is not static. In any event, your incoming load balancer IP wouldn't be used for outgoing connections.
You could assign elastic IPs to the actual instances behind the load balancer, which would then be used for outgoing requests. You get 5 free elastic ips, and I believe you can apply for more if you need them.
Additionally if using a VPC and if your instances are in a private subnet then they will only be able to access the internet via the NAT instance(s) you setup, and you can of course assign an elastic IP to the NAT instances
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