[Python] return 401 from lambda non-proxy api gateway and return headers

How do I return 401 to the client, based on the statusCode returned from the lambda? (non-proxy integration). How do I return the headers from the headers field? (for 401 and 200)

return {
"statusCode": 401,
"headers": {"myHeader": 'abcd "efg"'}
}


with this cdk:

unauthorized_integration_response = _api_gw.IntegrationResponse(
status_code="401",
response_parameters=response_integration_parameters,
selection_pattern='.*statusCode:401.*',
)
response_parameters = {
"method.response.header.Access-Control-Allow-Headers": True,
"method.response.header.Access-Control-Allow-Origin": True,
"method.response.header.Access-Control-Allow-Methods": True,
"method.response.header.Strict-Transport-Security": True,
"method.response.header.Content-Security-Policy": True,
"method.response.header.X-Frame-Options": True,
}
unauthorized_method_response = _api_gw.MethodResponse(
status_code="401", response_parameters=response_parameters
)

myresource.add_method(
"GET",
_api_gw.LambdaIntegration(
lambda_func,
proxy=False,
request_templates=default_request_template,
integration_responses=[
default_integration_response,
unauthorized_integration_response,
],
),
method_responses=[default_method_response, unauthorized_method_response],
)

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