Lambda Authorizer Cookies as identity source

Have you tried providing a token source header as mentioned here - https://docs.aws.amazon.com/apigateway/latest/developerguide/configure-api-gateway-lambda-authorization-with-console.html under point 9a - "Type the name of a header in Token Source. The API client must include a header of this name to send the authorization token to the Lambda authorizer."

yes, header.authorization works. but header.cookies does not work.

I have the same issue, I believe someone on the internet theorised that the implicit cloudfront in front of your rest api is blocking the cookie header. As far as I know there is no way to fix this for REST apis, the only option seems to be to setup a (regional?) HTTP api instead and use the v2 payload which includes cookie headers. Unfortunately the http api doesn't have some features of the rest api.