Http4k isn't an application framework, so it doesn't provide non-http integrations like SQL databases. I think people who are used to Spring tend to not really know how to integrate these things themselves, so if we want people to migrate, the least we can do is to help!
I support James' answer, but here's some additional information.
A single JDBC connection is usually enough for a Lambda, but if you know you need a connection pool per Lambda container, HikariCP is the defacto connection pool for JVM applications. You should look into its
documentation for guidance.
However, Amazon has a service called RDS Proxy that is specifically designed to pool connections for all your Lambda containers. I'm not an expert on it, but I believe it's incredibly useful even if your Lambdas only need a single connection, as it will make it faster for newly started lambdas to obtain their connection (someone can correct me if I'm wrong on this).
Personally, I prefer connectionless databases for AWS Lambda, like DynamoDB.