I have a Lambda function which can be triggered from an API gateway or ALB request. I also have an RDS Aurora PostgreSQL instance, both of which are running within a VPC.
I'm able to connect to the RDS instance from the Lambda just fine, however I can't access the internet, e.g. attempting to fire off a request to https://jsonplaceholder.typicode.com/todos/1 will cause a timeout.
I also can't connect to the remote database using a SQL client such as DBeaver.
Here's some detail below but let me know if you need anything else. I'm stumped.
Lambda Inbound Rules
Security group ID Ports Source sg-0f2c4426c8fc85235 80 0.0.0.0/0 sg-0f2c4426c8fc85235 5432 0.0.0.0/0 sg-0f2c4426c8fc85235 All sg-0f2c4426c8fc85235 sg-0f2c4426c8fc85235 22 0.0.0.0/0 sg-0f2c4426c8fc85235 443 0.0.0.0/0 Lambda Outbound Rules
Security group ID Ports Destination sg-0f2c4426c8fc85235 All 0.0.0.0/0 RDS Connectivity

VPC 
Public Subnet 
Private Subnet 
EDITS
Nat Gateway (associated with public subnet) 
Route Tables 
Route Table Routes 


EDIT 2
Lambda Subnets
