I am currently using the two Lambda functions (EchoCallerIP and UpdateHomeDNS) to effectively replace a DDNS provider. I have setup my own domain in Route 53 and exposed endpoints via AWS API Gateway to invoke these Lambda functions.
For convenience, I setup a "Custom Domain Name" in API Gateway to point the exposed API, and secured it with valid HTTPS certs with AWS Certificate Manager. This allows a clean and concise domain name, that I own, to point to my API.
Please note, the API Gateway endpoint that exposes the UpdateHomeDNS Lambda function is secured via API Key authentication on the API Gateway.