Logs from some loggers are not synced/flushed

**Issue**: when i use zerolog or zap loggers 60% of time logs are not synced, so they are not displayed in CloudWatch.

**Code of my handler**:
```go
var handlerInitialized = false
var chiAdapter *chiadapter.ChiLambda
var logger *zerolog.Logger

func Handler(req events.APIGatewayProxyRequest) (events.APIGatewayProxyResponse, error) {
if !handlerInitialized {
logger = zerolog.New(os.Stderr)
logger.Info("cold_start")

api := server.NewAPI(&logger)
chiAdapter = chiadapter.New(api.Router())
handlerInitialized = true
}

return chiAdapter.Proxy(req)
}

func main() {
lambda.Start(Handler)
}
```

used: https://github.com/awslabs/aws-lambda-go-api-proxy

Half of logs that comes from http Handlers and middlewares are not shown.

I found that only `standard logger` and `https://github.com/apex/log` work correctly.
I already asked this question in many places, and tried to use zap's `logger.Sync()` to flush, but it doesn't help.