The IP addresses of your load balancer aren't static. In any event, your incoming load balancer IP would not be used for outgoing connections.
You could assign elastic IPs to the particular instances behind the load balancer, which would then be used for outgoing requests. You get five free elastic IPs, and that I believe you'll apply for additional 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 set up, and you'll, in fact, assign an elastic IP to the NAT instances