Since there is an AWS Direct Connect connection between an Amazon VPC and your corporate network, the AWS Lambda function can be configured to connect to the VPC.
The Lambda function can then connect to the JIRA instance on the corporate network by using the private IP address of the JIRA instance.
You might be able to configure the VPC to defer to your corporate DNS server to resolve the DNS Name into the IP address, but I would recommend you start by using the private IP address itself to ensure that connectivity is working.