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.