In order to create Log Group and Log Stream Lambda execution role needs to have set of permissions enabled.
{
    "Statement": [
        {
            "Action": [
                "logs:CreateLogGroup",
                 "logs:CreateLogStream",
                 "logs:PutLogEvents"
            ],
            "Effect": "Allow",
            "Resource": "arn:aws:logs:*:*:*"
        }
    ]
} 
Once the necessary permissions are set it should work properly. You can check out AWS Documentation on Lambda function for more details.