A VPC in AWS is essentially a virtual datacenter.

For many years now, essentially all AWS services are tied to a VPC.

Each account gets 5 VPCs per region, by default.

Whether you use RDS or EC2 to setup a database server, it will be tied to a VPC for networking isolation purposes.

As such you then would need the Lambda in the VPC, or to allow public internet access to the database.

The point is pretty moot though, because you can schedule Cloudwatch Events every 4 minutes to keep a lambda warm, if necessary.

Frameworks like Zappa even do this for you automatically.