I am going to build a Lambda and a RDS aurora for my application. The RDS aurora needs to be inside a VPC and it doesn't need internet access. I have read a lot articles about VPC setup for database and all of them mentioned that need to create VPC, public/private subnets, route table, NAT gateway and internet gateway.
However, in my case, I don't need internet access in the database VPC. So my question is do I need NAT gateway and route table at all? I know each VPC has a default route table, is the default route table good enough? If I just create a VPC with 3 private subnets and attach the VPC to my lambda. Does it work?