How IP addresses get logged when using Lambda and API Gateway

You can enable Amazon CloudWatch Logs to trace API calls. Once enabled, API Gateway will log API calls in CloudWatch. The API gateway access log will have the information of the IP address "ip": "$context.identity.sourceIp":

https://docs.aws.amazon.com/apigateway/latest/developerguide/set-up-logging.html

Or check the value of "X-Forwarded-For" if you want to build a function in API Gateway by using Lambda Proxy integration:

https://docs.aws.amazon.com/apigateway/latest/developerguide/set-up-lambda-proxy-integrations.html