Cdk to add Http headers in lambda integration request

I have to add few http headers mapped to the context values comes from the lambda authorizer as shown below

"context": {
    "company_id": "xxxxx-xxx-xxxxxx",
    "Owner":"xxxxx",
  }

and the headers will be sent to the minimal api.

Can anyone help me on the cdk code(.ts) that send the custom headers to the .net api.