Access an Azure Synapse database from an AWS Lambda

I'd start by getting IP connectivity working but then I would expect that you'll need to setup "Hybrid DNS". Keep in-mind that the VPC+2 Route53 resolver is not accessible off the subnet; so, it will not be accessible from Azure. Please see my blog post How to achieve DNS high availability with Route 53 Resolver endpoints

Hello, You don't mention attaching your Lambda function to a VPC in your AWS account.

The Lambda service uses a Network Function Virtualization platform to provide NAT capabilities from the Lambda VPC to customer VPCs. This configures the required elastic network interfaces (ENIs) at the point where Lambda functions are created or updated. It also enables ENIs from your account to be shared across multiple execution environments, which allows Lambda to make more efficient use of a limited network resource when functions scale. Here are the instructions for Attaching Lambda functions to an Amazon VPC in your AWS account.

Since ENIs are an exhaustible resource and there is a soft limit of 250 ENIs per Region, you should monitor elastic network interface usage if you are configuring Lambda functions for VPC access. Generally, if you increase concurrency limits in Lambda, you should evaluate if you need an elastic network interface increase. If the limit is reached, this causes invocations of VPC-enabled Lambda functions to be throttled.

Here is the AWS Lambda - Operator Guide - Networking and VPC configurations

The article Understanding Azure Synapse Private Endpoints states: "When creating your workspace, you have the option to allow ALL IP address through." It seems like this is going to be needed in your environment.

Here are some how-to guides:

• Connect to workspace resources from a restricted network
• Connect to Azure Synapse Studio using Azure Private Link Hubs
• Connect to Azure Synapse Studio using Synapse Managed private endpoints

Note: The doc on Private Link Hubs states: "You must integrate the private endpoints with your DNS solution, either your on-premises solution or Azure Private DNS"

Here is a pair of great blogs on connecting AWS and Azure via VPN (over the internet):

• Multi-Cloud Enterprise Network Architectures — natively bridging AWS and Azure at scale (Part 1)
• Multi-Cloud Enterprise Network Architectures — natively bridging AWS and Azure at scale (Part 2)