If you are using multiple lambda functions to have the same execution role (not recommended) you should explicitly specify each lambda ARN in the resource of the cloudwatch policy. As an example:
{
"Version": "2012-10-17",
"Statement": [
{
"Effect": "Allow",
"Action": "logs:CreateLogGroup",
"Resource": "arn:aws:logs:REGION:ACCOUNT_ID:*"
},
{
"Effect": "Allow",
"Action": [
"logs:CreateLogStream",
"logs:PutLogEvents"
],
"Resource": [
"arn:aws:logs:REGION:ACCOUNT_ID:log-group:/aws/lambda/main_function:*",
"arn:aws:logs:REGION:ACCOUNT_ID:log-group:/aws/lambda/second_function:*"
]
}
]
}
This way your functions will be able to create log_group for each function.