I am looking to assign a static IP to my Lambda which is being invoked via the API gateway. This is required because, the downstream system that i invoke from this lambda accept
You can't assign a public/static IP to any Lambda function.
Your only good option is to deploy into a VPC with an Internet Gateway and configure routing from the Lambda's subnet through a NAT which has an Elastic IP. Then your target host can whitelist the Elastic IP.
Also see: