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The explanation is simple: A Lambda instance running in a VPC cannot access the internet:
When you add VPC configuration to a Lambda function, it can only access resources in that VPC. If a Lambda function needs to access both VPC resources and the public Internet, the VPC needs to have a Network Address Translation (NAT) instance inside the VPC.
The solution is also simple, if annoying: run a NAT Instance or NAT Gateway in the VPC. (An alternate solution is to take your Lambda out of the VPC, but that is a much bigger change.)
I am running Django / Zappa in Lambda with a NAT instance for connecting to Amazon Simple Email Service and it works fine.
Source:stackexchange.com