I have used API gateway to build business logic for my app that invokes the lambda function. For security assurance, I have generated a VAT report of the base URL of API from my cyber security expert. A total of 9 Vulnerabilities have been detected including Four Medium, three low-level, and two informational-level vulnerabilities have been identified.
One solution would be to integrate with AWS WAF for protecting your APIs against common web exploits.
https://docs.aws.amazon.com/apigateway/latest/developerguide/apigateway-control-access-aws-waf.html
irt custom headers: https://aws.amazon.com/premiumsupport/knowledge-center/custom-headers-api-gateway-lambda/