For most uses, database connection pooling (or, more accurately, keeping a connection per container), is the right practice to follow in Lambda. For many databases, creating a connection is expensive and slow, and amortizing those costs over multiple container uses (see https://aws.amazon.com/blogs/compute/container-reuse-in-lamb...) helps reduce latency and cost. Lambda allows you to configure a per-function concurrency limit, which you can use to make sure that the number of containers doesn't exceed your maximum database connections.