Connection pools always worked quite well with Lambdas, as long as the connection pool was initiated in the global scope of the running code, and not within the handler function. See [1] and [2]

[1] - https://docs.aws.amazon.com/lambda/latest/dg/running-lambda-...

[2] - https://blog.spotinst.com/2017/11/19/best-practices-serverle...