Lambdas are persistent so long as there is activity (ie it's "warm"). You can maintain a connection in a lambda and reuse it for subsequent calls. This isn't exactly the same as a connection pool, as you won't have multiplexing of any sort, but in practice you'll end up with 1 connection per concurrent request, which isn't too terrible, and if you keep the lambda warm there won't be any additional latency from having to connect.