You can redirect to a file the Lambda function writes out. But that sucks.
AWS Lambda is the perfect use case for something like dynamic image sizing. Except if you use it for that you'll force all your users to do a redirect when fetching images. No easy way to clean up when you do it that way either.
???
I guess this depends on your setup, but I don't see why you would have to do this. Lambda takes the image in, resizes them and uploads the result to S3.
If you use predictable S3 paths, your clients can just look those up. Of course, there are things you'll need to watch out for, but no redirects needed.
Any other webserver is simply get image off S3->Resize it->Send raw binary data to the user (and optionally cache the resized image if you think it'll be requested in that size again).
The Lambda flow is as follows. Get image off S3->Resize it->upload to S3 and then redirect the user to that image via a cloudfront URL.
Unnecessary steps caused by the inability of Lambda get binary data out through the API Gateway. Particularly from the users point of view. You double the number of requests they have to make to fetch images.
Lambda is great for running code in response to events (like SNS messages or S3 file uploads), but I really don't think it should be used for something like handling web requests. Just because you _can_ do something with a million steps and configuring 50 AWS services together, doesn't mean you _should_.
You're far better of sending out an SNS or an SQS triggered by an S3 object creation event.