Please see the following:
http://docs.aws.amazon.com/lambda/latest/dg/API_Invoke.html
LOGTYPE
You can set this optional parameter to Tail in the request only if you specify the InvocationType parameter with the value Response to the request. In this case, AWS Lambda returns the base64 encoding of the last 4 KB of log data generated by your lambda function in the x-amz-log-result header.
Valid Values: None | Tail
So, does this mean that any user with valid credentials to call a function can also read the logs that this function emits?
If so, this is an obvious vulnerability that could give an attacker some useful information about processing invalid input.
How do I configure the Amazon AWS Lambda feature to prevent log response in the response?
Update 1
1) Regarding the comment: "If a hacker can call your lambda function, you have more problems than looking at the log files."
Not true: Lambda functions should also be called directly from client code using the SDK.
For an example, see the figure below from the book AWS Lambda in Action:

2) Regarding the comment: “How exactly is this vulnerability? Only someone who provided AWS IAM credentials could call the Lambda function.”
Of course, customers usually have some credentials most of the time (for example, from logging into your mobile application with their Facebook account through Amazon Cognito). Should I trust all my users?
3) Regarding the comment: "Only if you entered some protected information for registration."
Magazines may contain reasonable information. I'm not talking about secure information, such as passwords, but just about helping the debugging team of the developers or the security team find out about the attacks. Applications can log all kinds of information, including the reason for the failure of some invalid input, which can help an attacker know what a valid input is. In addition, attackers can see all the information that the security team logs about their attacks. Not good. Even confidentiality may be at risk depending on what you register.
Update 2
This will also solve my problem if I could somehow find the Tail parameter in the Lambda code. Then I just fail with the message "The tail is now allowed." Unfortunately, the Context object does not seem to contain this information.