NAT Gateways in a VPC
You only need a NAT Gateway if your Lambda function will be accessing the internet. Assuming that you do need a NAT, you can just use one NAT Gateway for all your private subnets.
Want to know a secret? Even most Internet security gurus don’t remember a different password for every single site they use. But, they do use a different password for each site with the help of a Password Manager.