What is better for proxy and add athorization header to my calls? Lambda or Api Gateway

architecture
api-gateway
lambda
#1

Hello guys Im trying to decide among some architectures for my serverless application.
I have two backend endpoints in two different applications hosted on AWS and both of them need a static authorization header to work properly. So instead of creating a node server for my application just to proxy my same-origin requests and add the header Im thinking about doing that serverless.
What would you suggest me to do:
Front -> Api gateway -> my other endpoints
or
Front -> Lambda -> my other endpoints

I expect a high traffic for this application but the frontend call will always be over https, same origin and most of the time, by anonymous users

Thanks