Calling Private API from Lambda in VPC

Hi,

A customer is trying to invoke a private API Gateway from a Lambda in a VPC, there is a VPC endpoint configured in the VPC pointing to the private API Gateway. They are able to invoke the private API Gateway from an EC2 instance in the same VPC via the VPC endpoint, however if they try and do the same from the Lambda in the VPC they get no response. The resource policy on the private API Gateway is configured to allow all traffic from the VPC.

Does anyone know if this is a viable configuration and if so any references would be much appreciated. If this is not a viable configuration is it because the Lambda is actually in an AWS managed VPC so can't use the VPC endpoint in the customer VPC?

Even after a lot of searching I can't find any references to calling a private API Gateway from a Lambda so any help would be really appreciated