Send error message and stack to Lambda extension

dd-java-agent/instrumentation/aws-lambda-handler/src/main/java/datadog/trace/instrumentation/aws/v1/lambda/LambdaHandlerInstrumentation.java

@@ -112,6 +112,9 @@ static void exit(
 
       try {
         final AgentSpan span = scope.span();
+        if (throwable != null) {
+          span.addThrowable(throwable);
+        }
         span.finish();
         AgentTracer.get().notifyExtensionEnd(span, result, null != throwable);
       } finally {

dd-java-agent/instrumentation/aws-lambda-handler/src/test/groovy/HandlerStreamingWithError.java

@@ -0,0 +1,11 @@
+import com.amazonaws.services.lambda.runtime.Context;
+import com.amazonaws.services.lambda.runtime.RequestStreamHandler;
+import java.io.InputStream;
+import java.io.OutputStream;
+
+public class HandlerStreamingWithError implements RequestStreamHandler {
+  @Override
+  public void handleRequest(InputStream inputStream, OutputStream outputStream, Context context) {
+    throw new Error("Some error");
+  }
+}

dd-java-agent/instrumentation/aws-lambda-handler/src/test/groovy/LambdaHandlerInstrumentationTest.groovy

@@ -24,6 +24,40 @@ abstract class LambdaHandlerInstrumentationTest extends VersionedNamingTestBase
       }
     }
   }
+
+  def "test streaming handler with error"() {
+    when:
+    def input = new ByteArrayInputStream(StandardCharsets.UTF_8.encode("Hello").array())
+    def output = new ByteArrayOutputStream()
+    new HandlerStreamingWithError().handleRequest(input, output, null)
+
+    then:
+    thrown(Error)
+    assertTraces(1) {
+      trace(1) {
+        span {
+          operationName operation()
+          errored true
+          tags {
+            tag "error.type", "java.lang.Error"
+            tag "error.message", "Some error"
+            tag "error.stack", String
+            tag "language", "jvm"
+            tag "process_id", Long
+            tag "runtime-id", String
+            tag "thread.id", Long
+            tag "thread.name", String
+            tag "_dd.profiling.ctx", "test"
+            tag "_dd.profiling.enabled", 0
+            tag "_dd.agent_psr", 1.0
+            tag "_dd.tracer_host", String
+            tag "_sample_rate", 1
+            tag "_dd.trace_span_attribute_schema", { it != null }
+          }
+        }
+      }
+    }
+  }
 }