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You might need to add a lambda permission to allow eventbridge to invoke lambda:

{
  "Effect": "Allow",
  "Action": "lambda:InvokeFunction",
  "Resource": "arn:aws:lambda:_`region`_:_`account-id`_:function:_`function-name`_",
  "Principal": {
    "Service": "<http://events.amazonaws.com|events.amazonaws.com>"
  },
  "Condition": {
    "ArnLike": {
      "AWS:SourceArn": "arn:aws:events:_`region`_:_`account-id`_:rule/_`rule-name`_"
    }
  },
  "Sid": "InvokeLambdaFunction"
}