AWS lambda - best practice when reading from long list/s3

I have a scheduled error handling lambda, I would like to use Serverless technology here as opposed to a spring boot service or something.

The lambda will read from an s3 bucket and process accordingly. The problem is at times the s3 bucket may have high volume of data to be processed. long running operations aren't suited to lambdas.

One solution I can think of is have the lambda read and process one item from the bucket and on success trigger another instance of the same lambda unless the bucket is empty/fully-processed. The thing i don't like is that this is synchronous and quite slow. I also need to be conscious of running too many lambdas at the same time as we are hitting a REST endpoint as part of the error flow and don't want to overload it with too many requests.

I am thinking it would be nice to have maybe 3 instances of the lambdas running at the same time until the bucket is empty but not really sure, I am wondering if anyone has any nice patterns that could be used here or suggestions on best practices?

Thanks